On the maximal operator of the Marcinkiewicz-Fejér means of double Walsh - Kaczmarz - Fourier series

Ushangi Goginava; Károly Nagy

On the maximal operator of the Marcinkiewicz-Fejér means of double Walsh - Kaczmarz - Fourier series

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

Abstract

In the paper [3] we proved that the maximal operator of the Marcinkiewicz-Fejér means of the 2-dimensional Fourier series with respect to the Walsh-Kaczmarz system is not bounded from the Hardy space H _2/3 to the space L_2/3. Now, in this paper we prove a stronger result, that is there exists a martingale f ∈ H_2/3 such that the maximal Marcinkiewicz-Fejér operator with respect to Walsh-Kaczmarz system does not belong to the space L_2/3.

Original language	English
Pages (from-to)	95-104
Number of pages	10
Journal	Publicationes Mathematicae Debrecen
Volume	75
Issue number	1-2
Publication status	Published - 2009
Externally published	Yes

Keywords

Fejér means
Marcinkiewicz means
Maximal operator
Walsh-Kaczmarz system

ASJC Scopus subject areas

General Mathematics

Cite this

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AU - Goginava, Ushangi

AU - Nagy, Károly

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N2 - In the paper [3] we proved that the maximal operator of the Marcinkiewicz-Fejér means of the 2-dimensional Fourier series with respect to the Walsh-Kaczmarz system is not bounded from the Hardy space H 2/3 to the space L2/3. Now, in this paper we prove a stronger result, that is there exists a martingale f ∈ H2/3 such that the maximal Marcinkiewicz-Fejér operator with respect to Walsh-Kaczmarz system does not belong to the space L2/3.

AB - In the paper [3] we proved that the maximal operator of the Marcinkiewicz-Fejér means of the 2-dimensional Fourier series with respect to the Walsh-Kaczmarz system is not bounded from the Hardy space H 2/3 to the space L2/3. Now, in this paper we prove a stronger result, that is there exists a martingale f ∈ H2/3 such that the maximal Marcinkiewicz-Fejér operator with respect to Walsh-Kaczmarz system does not belong to the space L2/3.

KW - Fejér means

KW - Marcinkiewicz means

KW - Maximal operator

KW - Walsh-Kaczmarz system

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On the maximal operator of the Marcinkiewicz-Fejér means of double Walsh - Kaczmarz - Fourier series

Abstract

Keywords

ASJC Scopus subject areas

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