Unrestricted Cesàro summability of d-dimensional Fourier series and Lebesgue points

被引：7

作者：

Weisz, Ferenc ^{[1
]}

机构：

[1] Eotvos L Univ, Dept Numer Anal, Pazmany P Setany 1-C, H-1117 Budapest, Hungary

来源：

CONSTRUCTIVE MATHEMATICAL ANALYSIS | 2021年 / 4卷 / 02期

关键词：

Cesaro summability; strong Hardy-Littlewood maximal function; strong Lebesgue points; MARCINKIEWICZ-FEJER MEANS; EVERYWHERE CONVERGENCE; RESPECT;

D O I：

10.33205/cma.859583

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We generalize the classical Lebesgue's theorem to multi-dimensional functions. We prove that the Ces & agrave;ro means of the Fourier series of the multi-dimensional function f is an element of L-1(logL)(d-1)(T-d)superset of L-p(T-d)(1<p <=infinity) converge to f at each strong Lebesgue point.

引用

页码：179 / 185

页数：7

共 21 条

[1] SOME RECENT DEVELOPMENTS IN FOURIER-ANALYSIS AND HP-THEORY ON PRODUCT DOMAINS [J].

CHANG, SYA ;

FEFFERMAN, R .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1985, 12 (01) :1-43

[2] Wiener amalgams and pointwise summability of Fourier transforms and Fourier series [J].

Feichtinger, Hans G. ;

Weisz, Ferenc .

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 2006, 140 :509-536

[3]

Fejér L, 1904, MATH ANN, V58, P51

[4] Pointwise convergence of cone-like restricted two-dimensional (C, 1) means of trigonometric Fourier series [J].

Gat, Gyoergy .

JOURNAL OF APPROXIMATION THEORY, 2007, 149 (01) :74-102

[5] Almost everywhere convergence of sequences of CesA ro and Riesz means of integrable functions with respect to the multidimensional Walsh system [J].

Gat, Gyoergy .

ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2014, 30 (02) :311-322

[6] ON THE MARCINKIEWICZ-FEJER MEANS OF DOUBLE FOURIER SERIES WITH RESPECT TO THE WALSH-KACZMARZ SYSTEM [J].

Gat, Gyoergy ;

Goginava, Ushangi ;

Nagy, Karoly .

STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA, 2009, 46 (03) :399-421

[7] Marcinkiewicz-Fejer means of d-dimensional Walsh-Fourier series [J].

Goginava, U .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2005, 307 (01) :206-218

[8]

Goginava U., 2006, East J. Approx., V12, P295

[9] Almost everywhere convergence of (C, α)-means of cubical partial sums of d-dimensional Walsh-Fourier series [J].

Goginava, Ushangi .

JOURNAL OF APPROXIMATION THEORY, 2006, 141 (01) :8-28

[10]

Jessen B., 1935, Fundam. Math, V25, P217, DOI DOI 10.4064/FM-25-1-217-234

← 1 2 3 →