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jonasteuwenjonasteuwen
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Small fixes
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‎Gaussian-maximal-function.aux

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\providecommand\HyField@AuxAddToFields[1]{}
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\providecommand\HyField@AuxAddToCoFields[2]{}
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\abx@aux@sortscheme{nty}
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\abx@aux@cite{Pineda2008}
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\abx@aux@cite{Sjogren1997}
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\abx@aux@cite{Portal2012}
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\abx@aux@cite{Maas2011b}
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\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\select@language{english}}
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\@writefile{lof}{\defcounter {refsection}{0}\relax }\@writefile{lof}{\select@language{english}}
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\@writefile{lot}{\defcounter {refsection}{0}\relax }\@writefile{lot}{\select@language{english}}
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\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {section}{\tocsection {}{1}{The Mehler kernel and friends}}{1}{section.1}}
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\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {section}{\tocsection {}{1}{Introduction}}{1}{section.1}}
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\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{1.1}{Notation}}{1}{subsection.1.1}}
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\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{1.2}{Setting}}{1}{subsection.1.2}}
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\newlabel{eq:Ornstein-Uhlenbeck-operator}{{1}{1}{Setting}{equation.1.1}{}}
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\newlabel{eq:Ornstein-Uhlenbeck-semigroup-integral}{{2}{1}{Setting}{equation.1.2}{}}
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\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{1.3}{The Mehler kernel}}{1}{subsection.1.3}}
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\newlabel{eq:Mehler-kernel}{{3}{1}{The Mehler kernel}{equation.1.3}{}}
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\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {section}{\tocsection {}{2}{Some fine lemmata and definitions}}{1}{section.2}}
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\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{2.1}{$m$inimal function}}{1}{subsection.2.1}}
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\newlabel{lem:m-xy-equivalence-no-cone}{{1}{1}{}{lemma.1}{}}
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\newlabel{eq:Gaussian-cone}{{4}{2}{$m$inimal function}{equation.2.4}{}}
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\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {section}{\tocsection {}{2}{The Mehler kernel and friends}}{1}{section.2}}
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\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{2.1}{Setting}}{1}{subsection.2.1}}
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\newlabel{eq:Ornstein-Uhlenbeck-operator}{{1}{1}{Setting}{equation.2.1}{}}
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\newlabel{eq:Ornstein-Uhlenbeck-semigroup-integral}{{2}{1}{Setting}{equation.2.2}{}}
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\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{2.2}{The Mehler kernel}}{1}{subsection.2.2}}
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\newlabel{eq:Mehler-kernel}{{3}{1}{The Mehler kernel}{equation.2.3}{}}
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\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {section}{\tocsection {}{3}{Some fine lemmata and definitions}}{2}{section.3}}
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\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.1}{$m$inimal function}}{2}{subsection.3.1}}
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\newlabel{lem:m-xy-equivalence-no-cone}{{1}{2}{}{lemma.1}{}}
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\newlabel{eq:Gaussian-cone}{{4}{2}{$m$inimal function}{equation.3.4}{}}
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\newlabel{lem:m-xy-equivalence}{{2}{2}{}{lemma.2}{}}
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\newlabel{eq:Definition-local-region}{{5}{2}{}{equation.2.5}{}}
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\newlabel{eq:Definition-local-region-ball}{{6}{2}{}{equation.2.6}{}}
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\newlabel{eq:Definition-cut-off-set-D}{{7}{2}{$m$inimal function}{equation.2.7}{}}
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\newlabel{eq:Definition-local-region}{{5}{2}{}{equation.3.5}{}}
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\newlabel{eq:Definition-local-region-ball}{{6}{2}{}{equation.3.6}{}}
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\newlabel{eq:Definition-cut-off-set-D}{{7}{2}{$m$inimal function}{equation.3.7}{}}
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\newlabel{lem:Cone-Gaussians-comparable}{{3}{2}{}{lemma.3}{}}
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\newlabel{eq:Cone-Gaussians-comparable-1}{{8}{2}{$m$inimal function}{equation.2.8}{}}
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\newlabel{eq:Cone-Gaussians-comparable-2}{{9}{3}{$m$inimal function}{equation.2.9}{}}
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\newlabel{eq:Cone-Gaussians-comparable-1}{{8}{3}{$m$inimal function}{equation.3.8}{}}
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\newlabel{eq:Cone-Gaussians-comparable-2}{{9}{3}{$m$inimal function}{equation.3.9}{}}
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\newlabel{def:Global-region-cone-lemma}{{4}{3}{}{lemma.4}{}}
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\newlabel{eq:Global-region-cone-lemma-proof-1}{{10}{3}{$m$inimal function}{equation.2.10}{}}
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\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {section}{\tocsection {}{3}{On-diagonal estimates}}{3}{section.3}}
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\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.1}{Kernel estimates}}{3}{subsection.3.1}}
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\newlabel{lem:Time-part-Mehler-time-transform}{{5}{3}{}{lemma.5}{}}
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\newlabel{eq:Time-part-Mehler-time-transform}{{11}{3}{}{equation.3.11}{}}
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\newlabel{eq:Time-part-Mehler-time-transform-proof-1}{{12}{4}{Kernel estimates}{equation.3.12}{}}
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\newlabel{eq:Global-region-cone-lemma-proof-1}{{10}{3}{$m$inimal function}{equation.3.10}{}}
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\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {section}{\tocsection {}{4}{On-diagonal estimates}}{4}{section.4}}
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\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{4.1}{Kernel estimates}}{4}{subsection.4.1}}
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\newlabel{lem:Time-part-Mehler-time-transform}{{5}{4}{}{lemma.5}{}}
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\newlabel{eq:Time-part-Mehler-time-transform-1}{{11}{4}{}{equation.4.11}{}}
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\newlabel{eq:Time-part-Mehler-time-transform-2}{{12}{4}{}{equation.4.12}{}}
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\newlabel{eq:Time-part-Mehler-time-transform-proof-1}{{13}{4}{Kernel estimates}{equation.4.13}{}}
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\newlabel{lem:Exponential-estimates}{{6}{4}{}{lemma.6}{}}
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\newlabel{eq:Exponential-estimates-1}{{13}{4}{}{equation.3.13}{}}
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\newlabel{lem:Kernel-estimates-1}{{7}{4}{}{lemma.7}{}}
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\newlabel{eq:Kernel-lemma-1-estimate}{{14}{4}{}{equation.3.14}{}}
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\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.2}{On-diagonal kernel estimates on annuli}}{6}{subsection.3.2}}
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\newlabel{eq:C_k-annulus-decomposition}{{15}{6}{On-diagonal kernel estimates on annuli}{equation.3.15}{}}
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\newlabel{eq:C_k-annulus-decomposition-expand-nonzero}{{16}{6}{On-diagonal kernel estimates on annuli}{equation.3.16}{}}
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\newlabel{eq:C_k-annulus-decomposition-expand-zero}{{17}{6}{On-diagonal kernel estimates on annuli}{equation.3.17}{}}
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\newlabel{lem:On-diagonal-kernel-estimates-on-Ck}{{8}{6}{}{lemma.8}{}}
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\newlabel{lem:On-diagonal-kernel-estimates-on-Ck-proof-1}{{18}{6}{On-diagonal kernel estimates on annuli}{equation.3.18}{}}
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\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.3}{The Ornstein-Uhlenbeck maximal function}}{7}{subsection.3.3}}
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\newlabel{eq:Exponential-estimates-1}{{14}{4}{}{equation.4.14}{}}
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\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsubsection}{\tocsubsubsection {}{4.1.1}{Time-scaling of the Mehler kernel}}{5}{subsubsection.4.1.1}}
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\newlabel{lem:Kernel-estimates-1}{{7}{5}{}{lemma.7}{}}
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\newlabel{eq:Kernel-lemma-1-estimate}{{15}{5}{}{equation.4.15}{}}
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\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{4.2}{An estimate on Gaussian balls}}{6}{subsection.4.2}}
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\newlabel{lem:Gaussian-ball-shift-lemma}{{8}{6}{}{lemma.8}{}}
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\newlabel{eq:Gaussian-ball-shift-lemma}{{16}{6}{}{equation.4.16}{}}
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\newlabel{eq:Gaussian-ball-shift-lemma-proof-1}{{17}{6}{An estimate on Gaussian balls}{equation.4.17}{}}
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\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{4.3}{On-diagonal kernel estimates on annuli}}{6}{subsection.4.3}}
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\newlabel{eq:C_k-annulus-decomposition}{{18}{6}{On-diagonal kernel estimates on annuli}{equation.4.18}{}}
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\newlabel{eq:C_k-annulus-decomposition-expand}{{19}{6}{On-diagonal kernel estimates on annuli}{equation.4.19}{}}
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\newlabel{lem:On-diagonal-kernel-estimates-on-Ck}{{9}{6}{}{lemma.9}{}}
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\newlabel{lem:On-diagonal-kernel-estimates-on-Ck-proof-1}{{20}{7}{On-diagonal kernel estimates on annuli}{equation.4.20}{}}
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\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {section}{\tocsection {}{5}{The boundedness of some non-tangential maximal operators}}{7}{section.5}}
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\newlabel{lem:Maximal-function-cone}{{10}{7}{}{lemma.10}{}}
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\newlabel{eq:maximal_function_cone}{{21}{7}{}{equation.5.21}{}}
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\newlabel{eq:Mehler-kernel-estimate-one-sided-bound}{{22}{7}{The boundedness of some non-tangential maximal operators}{equation.5.22}{}}
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\newlabel{eq:Gaussian-ball-Maximal-function-cone-proof-1}{{23}{7}{The boundedness of some non-tangential maximal operators}{equation.5.23}{}}
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\newlabel{eq:Maximal-function-cone-intermediate-step-1}{{24}{8}{The boundedness of some non-tangential maximal operators}{equation.5.24}{}}
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\newlabel{tocindent-1}{0pt}
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\newlabel{tocindent0}{12.26888pt}
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\newlabel{tocindent1}{17.6065pt}
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\newlabel{tocindent2}{0pt}
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\newlabel{tocindent3}{0pt}
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\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {section}{\tocsection {}{}{References}}{8}{section*.1}}
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\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {section}{\tocsection {}{}{References}}{9}{section*.1}}

‎Gaussian-maximal-function.bbl

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\endverb
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\keyw{a,analisi armonica,analisi tempo-frequenza e,and the progetto cofinanziato,atomic hardy space,bmo,corresponding author,gauss measure,imaginary powers,laplaciani generalizzati,m,n,p,prin2005,project,riesz transform,singular integrals,teoria delle rappresentazioni,the italian g,work partially supported by}
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\endentry
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\entry{Pineda2008}{article}{}
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\name{labelname}{2}{}{%
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{{hash=3d00d353fffa98b253b1f66e05d098a4}{Pineda}{P\bibinitperiod}{E.}{E\bibinitperiod}{}{}{}{}}%
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{{hash=b4e29c4e79851084c81ed6bc7cddf72b}{Urbina}{U\bibinitperiod}{W.}{W\bibinitperiod}{}{}{}{}}%
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}
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\name{author}{2}{}{%
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{{hash=3d00d353fffa98b253b1f66e05d098a4}{Pineda}{P\bibinitperiod}{E.}{E\bibinitperiod}{}{}{}{}}%
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{{hash=b4e29c4e79851084c81ed6bc7cddf72b}{Urbina}{U\bibinitperiod}{W.}{W\bibinitperiod}{}{}{}{}}%
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}
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\strng{namehash}{23559c3d080caecee646487bdc719703}
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\strng{fullhash}{23559c3d080caecee646487bdc719703}
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\field{sortinit}{P}
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\field{labeltitle}{{Non Tangential Convergence for the Ornstein-Uhlenbeck Semigroup}}
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\field{journaltitle}{Divulgaciones Matemáticas}
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\field{number}{2}
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\field{title}{{Non Tangential Convergence for the Ornstein-Uhlenbeck Semigroup}}
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\field{volume}{13}
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\field{year}{2008}
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\field{pages}{1\bibrangedash 19}
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\verb{file}
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\verb :home/aw/teuwen/Localdisk/Mendeley-Desktop/Pineda, Urbina - 2008 - Non Tangential Convergence for the Ornstein-Uhlenbeck Semigroup.pdf:pdf
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\endverb
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\verb{url}
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\verb http://www.emis.ams.org/journals/DM/v16-1/art7.pdf
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\endverb
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\keyw{and phrases,hermite expansions,non tangential convergence,ornstein-,poisson-hermite semigroup,uhlenbeck semigroup}
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\endentry
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\entry{Portal2012}{unpublished}{}
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\name{labelname}{1}{}{%
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{{hash=72181505e073b35a6d75a96812fb827c}{Portal}{P\bibinitperiod}{Pierre}{P\bibinitperiod}{}{}{}{}}%

‎Gaussian-maximal-function.bcf

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<bcf:datasource type="file" datatype="bibtex">~/Documents/BibTeX/library.bib</bcf:datasource>
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</bcf:bibdata>
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<bcf:section number="0">
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<bcf:citekey order="1">Sjogren1997</bcf:citekey>
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<bcf:citekey order="2">Portal2012</bcf:citekey>
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<bcf:citekey order="3">Sjogren1997</bcf:citekey>
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<bcf:citekey order="4">Maas2011b</bcf:citekey>
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<bcf:citekey order="5">Mauceri2007</bcf:citekey>
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<bcf:citekey order="1">Pineda2008</bcf:citekey>
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<bcf:citekey order="2">Sjogren1997</bcf:citekey>
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<bcf:citekey order="3">Portal2012</bcf:citekey>
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<bcf:citekey order="4">Sjogren1997</bcf:citekey>
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<bcf:citekey order="5">Maas2011b</bcf:citekey>
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<bcf:citekey order="6">Mauceri2007</bcf:citekey>
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<bcf:citekey order="7">Pineda2008</bcf:citekey>
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</bcf:section>
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<bcf:sortlist section="0" type="entry" label="nty">
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<bcf:sorting>

‎Gaussian-maximal-function.blg

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[0] Config.pm:361> INFO - This is Biber 1.5
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[0] Config.pm:364> INFO - Logfile is 'Gaussian-maximal-function.blg'
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[107] biber:193> INFO - === Fri Jul 26, 2013, 13:27:36
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[107] Biber.pm:327> INFO - Reading 'Gaussian-maximal-function.bcf'
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‎Gaussian-maximal-function.fdb_latexmk

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"Gaussian-maximal-function.blg"
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["pdflatex"] 1374825139 "Gaussian-maximal-function.tex" "Gaussian-maximal-function.pdf" "Gaussian-maximal-function" 1374825140
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["pdflatex"] 1374840695 "Gaussian-maximal-function.tex" "Gaussian-maximal-function.pdf" "Gaussian-maximal-function" 1374840697
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