Uniform and Lconvergence of Logarithmic Means of WalshFourier Series

Authors
Gát, G. Goginava, U.
Citation
G. Gát, et U. Goginava,, Uniform and Lconvergence of Logarithmic Means of WalshFourier Series, Acta mathematica Sinica. English series (Print) , 22(2), 2006, pp. 497-506
Journal title
Acta mathematica Sinica. English series (Print) → ACNP
ISSN journal
14398516
Volume
22
Issue
2
Year of publication
2006
Pages
497 - 506
Database
ACNP
SICI code
Abstract
The (Nörlund) logarithmic means of the Fourier series of the integrable function f is: 1ln.k=1n.1Sk(f)n.k,whereln:=.k=1n.11k. In this paper we discuss some convergence and divergence properties of this logarithmic means of the Walsh.Fourier series of functions in the uniform, and in the L1 Lebesgue norm. Among others, as an application of our divergence results we give a negative answer to a question of Móricz concerning the convergence of logarithmic means in norm