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ArticleOriginal scientific text

Title

Strong convergence theorems for two-parameter Walsh-Fourier and trigonometric-Fourier series

Authors 1

Affiliations

  1. Department of Numerical Analysis, Eötvös L. University, Múzeum krt. 6-8, H-1088 Budapest, Hungary

Abstract

The martingale Hardy space Hp([0,1)2) and the classical Hardy space Hp(^2) are introduced. We prove that certain means of the partial sums of the two-parameter Walsh-Fourier and trigonometric-Fourier series are uniformly bounded operators from Hp to Lp (0 < p ≤ 1). As a consequence we obtain strong convergence theorems for the partial sums. The classical Hardy-Littlewood inequality is extended to two-parameter Walsh-Fourier and trigonometric-Fourier coefficients. The dual inequalities are also verified and a Marcinkiewicz-Zygmund type inequality is obtained for BMO spaces.

Keywords

ENG
martingale and classical Hardy spaces, p-atom, atomic decomposition, Walsh functions, Hardy-Littlewood inequality

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Studia Mathematica
1995-1996/117/2
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Pages:
173-194
Main language of publication
English
Received
1995-05-05
Published
1996
Exact and natural sciences