On (Hpq, Lpq)-type inequality of maximal operator of marcinkiewicz-fejér means of double fourier series with respect to the Kaczmarz system

G. Gát; U. Goginava; K. Nagy

doi:10.7153/mia-09-46

On (H_pq, L_pq)-type inequality of maximal operator of marcinkiewicz-fejér means of double fourier series with respect to the Kaczmarz system

G. Gát, U. Goginava, K. Nagy

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

6 Citations (Scopus)

Abstract

The main aim of this paper is to prove that the maximal operator of Marcinkiewicz-Fejér means of double Fourier series with respect to the Kaczmarz system is bounded from the dyadic Hardy-Lorentz space H_pq into the Lorentz space L_pq for every p > 1/2 and 0 < g ≤ ∞ provided that the supremum in the maximal operator is taken over special indices. As a consequence, we obtain the a.e. convergence of Marcinkiewicz-Fejér means of double Fourier series for special indices with respect to the Walsh-Kaczmarz system. That is, σ_2n (f, x¹, x²) → f(x¹, x²) a.e. as n → ∞.

Original language	English
Pages (from-to)	473-483
Number of pages	11
Journal	Mathematical Inequalities and Applications
Volume	9
Issue number	3
DOIs	https://doi.org/10.7153/mia-09-46
Publication status	Published - Jul 2006
Externally published	Yes

Keywords

Marcinkiewicz-Fejér means
Maximal operator
Walsh-Kaczmarz system

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

Access to Document

10.7153/mia-09-46

Cite this

@article{4d1215ac98264f1d9b099ebbd4e54bc6,

title = "On (Hpq, Lpq)-type inequality of maximal operator of marcinkiewicz-fej{\'e}r means of double fourier series with respect to the Kaczmarz system",

abstract = "The main aim of this paper is to prove that the maximal operator of Marcinkiewicz-Fej{\'e}r means of double Fourier series with respect to the Kaczmarz system is bounded from the dyadic Hardy-Lorentz space Hpq into the Lorentz space Lpq for every p > 1/2 and 0 < g ≤ ∞ provided that the supremum in the maximal operator is taken over special indices. As a consequence, we obtain the a.e. convergence of Marcinkiewicz-Fej{\'e}r means of double Fourier series for special indices with respect to the Walsh-Kaczmarz system. That is, σ2n (f, x1, x2) → f(x1, x2) a.e. as n → ∞.",

keywords = "Marcinkiewicz-Fej{\'e}r means, Maximal operator, Walsh-Kaczmarz system",

author = "G. G{\'a}t and U. Goginava and K. Nagy",

year = "2006",

month = jul,

doi = "10.7153/mia-09-46",

language = "English",

volume = "9",

pages = "473--483",

journal = "Mathematical Inequalities and Applications",

issn = "1331-4343",

publisher = "Element d.o.o.",

number = "3",

}

TY - JOUR

T1 - On (Hpq, Lpq)-type inequality of maximal operator of marcinkiewicz-fejér means of double fourier series with respect to the Kaczmarz system

AU - Gát, G.

AU - Goginava, U.

AU - Nagy, K.

PY - 2006/7

Y1 - 2006/7

N2 - The main aim of this paper is to prove that the maximal operator of Marcinkiewicz-Fejér means of double Fourier series with respect to the Kaczmarz system is bounded from the dyadic Hardy-Lorentz space Hpq into the Lorentz space Lpq for every p > 1/2 and 0 < g ≤ ∞ provided that the supremum in the maximal operator is taken over special indices. As a consequence, we obtain the a.e. convergence of Marcinkiewicz-Fejér means of double Fourier series for special indices with respect to the Walsh-Kaczmarz system. That is, σ2n (f, x1, x2) → f(x1, x2) a.e. as n → ∞.

AB - The main aim of this paper is to prove that the maximal operator of Marcinkiewicz-Fejér means of double Fourier series with respect to the Kaczmarz system is bounded from the dyadic Hardy-Lorentz space Hpq into the Lorentz space Lpq for every p > 1/2 and 0 < g ≤ ∞ provided that the supremum in the maximal operator is taken over special indices. As a consequence, we obtain the a.e. convergence of Marcinkiewicz-Fejér means of double Fourier series for special indices with respect to the Walsh-Kaczmarz system. That is, σ2n (f, x1, x2) → f(x1, x2) a.e. as n → ∞.

KW - Marcinkiewicz-Fejér means

KW - Maximal operator

KW - Walsh-Kaczmarz system

UR - http://www.scopus.com/inward/record.url?scp=33747068010&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33747068010&partnerID=8YFLogxK

U2 - 10.7153/mia-09-46

DO - 10.7153/mia-09-46

M3 - Article

AN - SCOPUS:33747068010

SN - 1331-4343

VL - 9

SP - 473

EP - 483

JO - Mathematical Inequalities and Applications

JF - Mathematical Inequalities and Applications

IS - 3

ER -