Maximal operators of Fejér means of Walsh-Kaczmarz-Fourier series

Ushangi Goginava; Károly Nagy

doi:10.1155/2010/638327

Maximal operators of Fejér means of Walsh-Kaczmarz-Fourier series

Ushangi Goginava, Károly Nagy

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

2 Citations (Scopus)

Abstract

The main aim of this paper is to prove that there exists a martingale f ∈ H _1/2 such that the maximal Fejér operator with respect to Walsh-Kaczmarz system does not belong to the space L _1/2. For the two-dimensional case, we prove that there exists a martingale f ∈ H ^□ _1/2(f ∈ H _1/2) such that the restricted (unrestricted) maximal operator of Fejér means of two-dimensional Walsh-Kaczmarz-Fourier series does not belong to the space weak-L _1/2.

Original language	English
Pages (from-to)	181-200
Number of pages	20
Journal	Journal of Function Spaces and Applications
Volume	8
Issue number	2
DOIs	https://doi.org/10.1155/2010/638327
Publication status	Published - 2010
Externally published	Yes

Keywords

Fejér means
Hardy space
Walsh Kaczmarz system

ASJC Scopus subject areas

Analysis

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10.1155/2010/638327

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abstract = "The main aim of this paper is to prove that there exists a martingale f ∈ H 1/2 such that the maximal Fej{\'e}r operator with respect to Walsh-Kaczmarz system does not belong to the space L 1/2. For the two-dimensional case, we prove that there exists a martingale f ∈ H □ 1/2(f ∈ H 1/2) such that the restricted (unrestricted) maximal operator of Fej{\'e}r means of two-dimensional Walsh-Kaczmarz-Fourier series does not belong to the space weak-L 1/2.",

keywords = "Fej{\'e}r means, Hardy space, Walsh Kaczmarz system",

author = "Ushangi Goginava and K{\'a}roly Nagy",

year = "2010",

doi = "10.1155/2010/638327",

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pages = "181--200",

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AU - Goginava, Ushangi

AU - Nagy, Károly

PY - 2010

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N2 - The main aim of this paper is to prove that there exists a martingale f ∈ H 1/2 such that the maximal Fejér operator with respect to Walsh-Kaczmarz system does not belong to the space L 1/2. For the two-dimensional case, we prove that there exists a martingale f ∈ H □ 1/2(f ∈ H 1/2) such that the restricted (unrestricted) maximal operator of Fejér means of two-dimensional Walsh-Kaczmarz-Fourier series does not belong to the space weak-L 1/2.

AB - The main aim of this paper is to prove that there exists a martingale f ∈ H 1/2 such that the maximal Fejér operator with respect to Walsh-Kaczmarz system does not belong to the space L 1/2. For the two-dimensional case, we prove that there exists a martingale f ∈ H □ 1/2(f ∈ H 1/2) such that the restricted (unrestricted) maximal operator of Fejér means of two-dimensional Walsh-Kaczmarz-Fourier series does not belong to the space weak-L 1/2.

KW - Fejér means

KW - Hardy space

KW - Walsh Kaczmarz system

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Maximal operators of Fejér means of Walsh-Kaczmarz-Fourier series

Abstract

Keywords

ASJC Scopus subject areas

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