Universal functions for classes Lp[0,1)2, p∈(0,1), with respect to the double Walsh system

被引：0

作者：

Sargsyan, Artsrun ^{[1
]}

Grigoryan, Martin ^{[2
]}

机构：

[1] RAU, 123 Hovsep Emin Str, Yerevan 0051, Armenia

[2] YSU, 1 Alex Manoogian Str, Yerevan 0025, Armenia

来源：

POSITIVITY | 2019年 / 23卷 / 05期

关键词：

Universal function; Universal series; Fourier coefficients; Walsh system; Convergence in metric; SERIES; REPRESENTATION; DIVERGENCE;

D O I：

10.1007/s11117-019-00663-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In the paper it is shown that there exists a function U is an element of L1[0,1)2, which is universal for all class Lp[0,1)2, p is an element of(0,1), by rectangles and by spheres with respect to the double Walsh system in the sense of signs of Fourier coefficients.

引用

页码：1261 / 1280

页数：20

共 37 条

[1] ON THE STRUCTURE OF UNIVERSAL FUNCTIONS FOR CLASSES Lp[0,1)2, p ∈ (0,1), WITH RESPECT TO THE DOUBLE WALSH SYSTEM
Grigoryan, Martin
Sargsyan, Artsrun
BANACH JOURNAL OF MATHEMATICAL ANALYSIS, 2019, 13 (03): : 647 - 674
[2] On the universal function for the class LP[0,1], p ∈ (0,1)
Grigoryan, M. G.
Sargsyan, A. A.
JOURNAL OF FUNCTIONAL ANALYSIS, 2016, 270 (08) : 3111 - 3133
[3] The structure of universal functions for Lp-spaces, p ∈(0,1)
Grigoryan, Martin G.
Sargsyan, Artsrun A.
SBORNIK MATHEMATICS, 2018, 209 (01) : 35 - 55
[4] Quasiuniversal Fourier-Walsh Series for the Classes Lp[0,1], p > 1
Sargsyan, A. A.
MATHEMATICAL NOTES, 2018, 104 (1-2) : 278 - 292
[5] Universal Functions with Respect to the Double Walsh System for Classes of Integrable Functions
Sargsyan, A.
Grigoryan, M.
ANALYSIS MATHEMATICA, 2020, 46 (02) : 367 - 392
[6] On existence of a universal function for L p [0,1] with p ∈(0,1)
Grigoryan, M. G.
Sargsyan, A. A.
SIBERIAN MATHEMATICAL JOURNAL, 2016, 57 (05) : 796 - 808
[7] Universal function for a weighted space Lμ1 [0,1]
Sargsyan, Artsrun
Grigoryan, Martin
POSITIVITY, 2017, 21 (04) : 1457 - 1482
[8] ON THE UNIVERSAL FUNCTION FOR WEIGHTED SPACES Lμp[0,1], p ≥ 1
Grigoryan, Martin
Grigoryan, Tigran
Sargsyan, Artsrun
BANACH JOURNAL OF MATHEMATICAL ANALYSIS, 2018, 12 (01): : 104 - 125
[9] ON THE EXISTENCE OF UNIVERSAL FUNCTIONS WITH RESPECT TO THE DOUBLE WALSH SYSTEM FOR CLASSES OF INTEGRABLE FUNCTIONS
Sargsyan, Artsrun
COLLOQUIUM MATHEMATICUM, 2020, 161 (01) : 111 - 129
[10] Universal functions for classes Lp[0,1)2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^p[0,1)^2$$\end{document}, p∈(0,1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p\in (0,1)$$\end{document}, with respect to the double Walsh system
Artsrun Sargsyan
Martin Grigoryan
Positivity, 2019, 23 (5) : 1261 - 1280

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