Strong convergence of two-dimensional Vilenkin-Fourier series
نویسندگان
چکیده
منابع مشابه
Convergence and Divergence of Fejér Means of Fourier Series on One and Two-Dimensional Walsh and Vilenkin Groups
It is a highly celebrated issue in dyadic harmonic analysis the pointwise convergence of the Fejér (or (C,1)) means of functions on the Walsh and Vilenkin groups both in the point of view of one and two dimensional cases. We give a résumé of the very recent developments concerning this matter, propose unsolved problems and throw a glance at the investigation of Vilenkin-like systems too.
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Abstract: The main aim of this paper is to prove that the maximal operator of a subsequence of the (one-dimensional) logarithmic means of Vilenkin-Fourier series is of weak type (1,1). Moreover, we prove that the maximal operator of the logarithmic means of quadratical partial sums of double Vilenkin-Fourier series is of weak type (1,1), provided that the supremum in the maximal operator is tak...
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The main aim of this paper is to investigate (Hp, Lp)-type inequalities for maximal operators of logarithmic means of one-dimensional bounded Vilenkin-Fourier series.
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ژورنال
عنوان ژورنال: Mathematische Nachrichten
سال: 2015
ISSN: 0025-584X
DOI: 10.1002/mana.201400239