On the Fourier-Haar coefficients of functions of several variables with bounded Vitali variation

被引：0

作者：

Galkina, SY ^{[1
]}

机构：

[1] Nizhnii Novgorod State Pedagog Univ, Nizhnii Novgorod, Russia

来源：

MATHEMATICAL NOTES | 2001年 / 70卷 / 5-6期

关键词：

Fourier-Haar coefficients; function of bounded variation; Vitali variation of functions of several variables; Haar system; Fubini's theorem;

D O I：

10.1023/A:1012951615759

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study the behavior of the Fourier-Haar coefficients a(m1),...,m(n)(f) of functions f Lebesgue integrable on the n-dimensional cube D, = [0,1](n) and having a bounded Vitali variation V(Dn)f on it. It is proved that Sigma(m1=2)(infinity ...) Sigma(mn=2)(infinity) \a(m1),...,m(n)(f)\ less than or equal to (2+root2/3)(n.)v(Dn)f and shown that this estimate holds for some function of bounded finite nonzero Vitali variation.

引用

页码：733 / 743

页数：11

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