Geodesic
On the maximal operator of Walsh-Kaczmarz-Fejér means
Czechoslovak Mathematical Journal, Tome 61 (2011) no. 3, pp. 673-686
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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 $L_{1/2}( G).$
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 $L_{1/2}( G).$
DOI : 10.1007/s10587-011-0038-6
Classification : 42B25, 42C10
Keywords: Walsh-Kaczmarz system; Fejér means; maximal operator 
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Goginava, Ushangi; Nagy, Károly. On the maximal operator of Walsh-Kaczmarz-Fejér means. Czechoslovak Mathematical Journal, Tome 61 (2011) no. 3, pp. 673-686. doi: 10.1007/s10587-011-0038-6

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