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On the logarithmic summability of Fourier series
-
György Gát
and
Károly Nagy
Published/Copyright:
May 2, 2011
Abstract
In 2005, Tkebuchava constructed a set of logarithmic summation methods which includes Riesz and Nörlund logarithmic summation methods as limit cases. He gave estimates for the kernels of a trigonometric system and also some consequences with respect to the convergence of the means of a Fourier series. Here we give such good estimates for the kernels with respect to Walsh and Walsh–Kaczmarz systems as Tkebuchava did.
Keywords.: Logarithmic means; Nörlund logarithmic means; Walsh group; Walsh system; Walsh–Kaczmarz system
Received: 2009-02-05
Published Online: 2011-05-02
Published in Print: 2011-June
© de Gruyter 2011
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Keywords for this article
Logarithmic means;
Nörlund logarithmic means;
Walsh group;
Walsh system;
Walsh–Kaczmarz system
Articles in the same Issue
- Polynomial approximation of functions in weighted Lebesgue and Smirnov spaces with nonstandard growth
- On the logarithmic summability of Fourier series
- On a relationship between absolutely nonmeasurable functions and Sierpiński–Zygmund functions
- Boundedness of weighted singular integral operators in grand Lebesgue spaces
- A generalization of the Euler beta function and applications
- Normality and shared values concerning differential polynomial
- Fixed point theorems for singlevalued and multivalued generalized contractions in metric spaces endowed with a graph
- About some geometric characteristics of the generalized Möbius–Listing surfaces
- Variation formulas of solution for a delay differential equation taking into account delay perturbation and the continuous initial condition
- An admissibility for topological degree of variable Besov and Triebel–Lizorkin spaces
- Boundedness of linear operators via atoms on Hardy spaces with non-doubling measures
