Weak type inequality for logarithmic means of Walsh-Kaczmarz-Fourier series

Ushangi Goginava; Károly Nagy

doi:10.14321/realanalexch.35.2.0445

Weak type inequality for logarithmic 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 the Nörlund logarithmic means t_n^κ f of one-dimensional Walsh-Kaczmarz-Fourier series is weak type (1,1), and this fact implies that t_n^κf converges in measure on I for every function f ∈ L(I) and t_n,m^κ f converges in measure on I² for every function f ∈ Lln⁺ L(I²): Moreover, the maximal Orlich space such that Nörlund logarithmic means of two-dimensional Walsh-Kaczmarz-Fourier series for the functions from this space converge in two-dimensional measure is found.

Original language	English
Pages (from-to)	445-462
Number of pages	18
Journal	Real Analysis Exchange
Volume	35
Issue number	2
DOIs	https://doi.org/10.14321/realanalexch.35.2.0445
Publication status	Published - 2010
Externally published	Yes

Keywords

Convergence in measure
Double Walsh-Kaczmarz-Fourier series
Orlicz space

ASJC Scopus subject areas

Analysis
Geometry and Topology

Access to Document

10.14321/realanalexch.35.2.0445

Cite this

@article{82baf9bfce194c42b5d2eda5952a57c8,

title = "Weak type inequality for logarithmic means of Walsh-Kaczmarz-Fourier series",

abstract = "The main aim of this paper is to prove that the N{\"o}rlund logarithmic means tnκ f of one-dimensional Walsh-Kaczmarz-Fourier series is weak type (1,1), and this fact implies that tnκf converges in measure on I for every function f ∈ L(I) and tn,mκ f converges in measure on I2 for every function f ∈ Lln+ L(I2): Moreover, the maximal Orlich space such that N{\"o}rlund logarithmic means of two-dimensional Walsh-Kaczmarz-Fourier series for the functions from this space converge in two-dimensional measure is found.",

keywords = "Convergence in measure, Double Walsh-Kaczmarz-Fourier series, Orlicz space",

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

year = "2010",

doi = "10.14321/realanalexch.35.2.0445",

language = "English",

volume = "35",

pages = "445--462",

journal = "Real Analysis Exchange",

issn = "0147-1937",

publisher = "Michigan State University Press",

number = "2",

}

TY - JOUR

T1 - Weak type inequality for logarithmic means of Walsh-Kaczmarz-Fourier series

AU - Goginava, Ushangi

AU - Nagy, Károly

PY - 2010

Y1 - 2010

N2 - The main aim of this paper is to prove that the Nörlund logarithmic means tnκ f of one-dimensional Walsh-Kaczmarz-Fourier series is weak type (1,1), and this fact implies that tnκf converges in measure on I for every function f ∈ L(I) and tn,mκ f converges in measure on I2 for every function f ∈ Lln+ L(I2): Moreover, the maximal Orlich space such that Nörlund logarithmic means of two-dimensional Walsh-Kaczmarz-Fourier series for the functions from this space converge in two-dimensional measure is found.

AB - The main aim of this paper is to prove that the Nörlund logarithmic means tnκ f of one-dimensional Walsh-Kaczmarz-Fourier series is weak type (1,1), and this fact implies that tnκf converges in measure on I for every function f ∈ L(I) and tn,mκ f converges in measure on I2 for every function f ∈ Lln+ L(I2): Moreover, the maximal Orlich space such that Nörlund logarithmic means of two-dimensional Walsh-Kaczmarz-Fourier series for the functions from this space converge in two-dimensional measure is found.

KW - Convergence in measure

KW - Double Walsh-Kaczmarz-Fourier series

KW - Orlicz space

UR - https://www.scopus.com/pages/publications/84864939518

UR - https://www.scopus.com/pages/publications/84864939518#tab=citedBy

U2 - 10.14321/realanalexch.35.2.0445

DO - 10.14321/realanalexch.35.2.0445

M3 - Article

AN - SCOPUS:84864939518

SN - 0147-1937

VL - 35

SP - 445

EP - 462

JO - Real Analysis Exchange

JF - Real Analysis Exchange

IS - 2

ER -

Weak type inequality for logarithmic means of Walsh-Kaczmarz-Fourier series

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this