Open AccessCESARO SUMMABILITY OF WALSH-FOURIER SERIES
Author(s) -
N. J. Fine
Publication year - 1955
Publication title -
proceedings of the national academy of sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 5.011
H-Index - 771
eISSN - 1091-6490
pISSN - 0027-8424
DOI - 10.1073/pnas.41.8.588
Subject(s) - gene , context (archaeology) , gene expression , biology , adaptive evolution , series (stratigraphy) , expression (computer science) , genetics , genetic variation , evolutionary biology , computer science , paleontology , programming language
summary:In this paper we prove that the maximal operator $$\tilde {\sigma }^{\kappa ,*}f:=\sup _{n\in {\mathbb P}}\frac {|{\sigma }_n^\kappa f|}{\log ^{2}(n+1)},$$ where ${\sigma }_n^\kappa f$ is the $n$-th Fejér mean of the Walsh-Kaczmarz-Fourier series, is bounded from the Hardy space $H_{1/2}( G) $ to the space $L_{1/2}( G).
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