The weak type inequality for the maximal operator of the marcenkiewicz-fejer means of the two-dimensional walsh-kaczmarz system

Ushangi Goginava

doi:10.7153/mia-12-19

The weak type inequality for the maximal operator of the marcenkiewicz-fejer means of the two-dimensional walsh-kaczmarz system

Ushangi Goginava

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

1 Citation (Scopus)

Abstract

The main aim of this paper is to prove that the maximal operator σ^# of the Marcin-kiewicz-Fejer means of the two-dimensional Fourier series with respect to the Walsh-Kaczmarz system is bounded from the martingale Hardy space H_1/2 to the space weak-L_1/2 and is not bounded from the martingale Hardy space H_1/2 to the space L _1/2 provided that the supremum in the maximal operator is taken over spatial indices.

Original language	English
Pages (from-to)	227-238
Number of pages	12
Journal	Mathematical Inequalities and Applications
Volume	12
Issue number	2
DOIs	https://doi.org/10.7153/mia-12-19
Publication status	Published - Apr 2009
Externally published	Yes

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.7153/mia-12-19

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abstract = "The main aim of this paper is to prove that the maximal operator σ\# of the Marcin-kiewicz-Fejer means of the two-dimensional Fourier series with respect to the Walsh-Kaczmarz system is bounded from the martingale Hardy space H1/2 to the space weak-L1/2 and is not bounded from the martingale Hardy space H1/2 to the space L 1/2 provided that the supremum in the maximal operator is taken over spatial indices.",

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The weak type inequality for the maximal operator of the marcenkiewicz-fejer means of the two-dimensional walsh-kaczmarz system

Abstract

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