On the boundedness of the maximal operators of double Walsh-logarithmic means of Marcinkiewicz type

被引：0

作者：

Goginava, Ushangi ^{[1
]}

Nagy, Karoly ^{[2
]}

机构：

[1] Fac Exact & Nat Sci, Inst Math, Tbilisi 0128, Georgia

[2] Coll Nyiregyhaza, Inst Math & Comp Sci, H-4400 Nyiregyhaza, Hungary

来源：

MATHEMATICA SLOVACA | 2013年 / 63卷 / 04期

基金：

美国国家科学基金会;

关键词：

Walsh system; Hardy space; logarithmic means; Norlund means; double Walsh-Fourier series; FEJER MEANS; FOURIER; CONVERGENCE; SUMMABILITY;

D O I：

10.2478/s12175-013-0138-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The main aim of this paper is to investigate the (H (p) , L (p) )-type inequality for the maximal operators of Riesz and Norlund logarithmic means of the quadratical partial sums of Walsh-Fourier series. Moreover, we show that the behavior of Norlund logarithmic means is worse than the behavior of Riesz logarithmic means in our special sense.

引用

页码：839 / 848

页数：10

共 11 条

[1] [Anonymous], 1996, Anal.Math., V22, P229, DOI DOI 10.1007/BF02205221
[2] Convergence in measure of logarithmic means of quadratical partial sums of double Walsh-Fourier series
Gat, G.
Goginava, U.
Tkebuchava, G.
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 323 (01) : 535 - 549
[3] Uniform and L-convergence of logarithmic means of walsh-fourier series
Gát, G
Goginava, U
[J]. ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2006, 22 (02) : 497 - 506
[4] Gat G., 2004, E J APPROX, V10, P391
[5] Goginava U, 2007, PUBL MATH-DEBRECEN, V71, P43
[6] The weak type inequality for the maximal operator of the Marcinkiewicz-Fejer means of the two-dimensional Walsh-Fourier series
Goginava, Ushangi
[J]. JOURNAL OF APPROXIMATION THEORY, 2008, 154 (02) : 161 - 180
[7] Schipp F., 1990, WALSH SERIES INTRO D
[8] Weak inequalities for Cesaro and Riesz summability of Walsh-Fourier series
Simon, Peter
Weisz, Ferenc
[J]. JOURNAL OF APPROXIMATION THEORY, 2008, 151 (01) : 1 - 19
[9] θ-summability of Fourier series
Weisz, F
[J]. ACTA MATHEMATICA HUNGARICA, 2004, 103 (1-2) : 139 - 175
[10] Weisz F., 2001, Approx. Theory Appl. (N. S.), V17, P32

← 1 2 →