The martingale hardy type inequality for Marcinkiewicz-Fejér means of two-dimensional conjugate Walsh-Fourier series

Ushangi Goginava

doi:10.1007/s10114-011-9551-7

The martingale hardy type inequality for Marcinkiewicz-Fejér means of two-dimensional conjugate Walsh-Fourier series

Ushangi Goginava

Research output: Contribution to journal › Article › peer-review

13 Citations (Scopus)

Abstract

The main aim of this paper is to prove that for any 0 < p ≤ 2/3 there exists a martingale f ∈ H_p such that Marcinkiewicz-Fejér means of the two-dimensional conjugate Walsh-Fourier series of the martingale f is not uniformly bounded in the space L_p.

Original language	English
Pages (from-to)	1949-1958
Number of pages	10
Journal	Acta Mathematica Sinica, English Series
Volume	27
Issue number	10
DOIs	https://doi.org/10.1007/s10114-011-9551-7
Publication status	Published - Oct 2011
Externally published	Yes

Keywords

Marcinkiewicz-Fejér means
martingale Hardy space
Two-dimensional Walsh-Fourier series

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1007/s10114-011-9551-7

Cite this

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title = "The martingale hardy type inequality for Marcinkiewicz-Fej{\'e}r means of two-dimensional conjugate Walsh-Fourier series",

abstract = "The main aim of this paper is to prove that for any 0 < p ≤ 2/3 there exists a martingale f ∈ Hp such that Marcinkiewicz-Fej{\'e}r means of the two-dimensional conjugate Walsh-Fourier series of the martingale f is not uniformly bounded in the space Lp.",

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AB - The main aim of this paper is to prove that for any 0 < p ≤ 2/3 there exists a martingale f ∈ Hp such that Marcinkiewicz-Fejér means of the two-dimensional conjugate Walsh-Fourier series of the martingale f is not uniformly bounded in the space Lp.

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KW - Two-dimensional Walsh-Fourier series

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The martingale hardy type inequality for Marcinkiewicz-Fejér means of two-dimensional conjugate Walsh-Fourier series

Abstract

Keywords

ASJC Scopus subject areas

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