Order of magnitude of multiple Fourier coefficients of functions of bounded variation

被引：15

作者：

Fülöp, V ^{[1
]}

Móricz, F ^{[1
]}

机构：

[1] Univ Szeged, Bolyai Inst, H-6720 Szeged, Hungary

来源：

ACTA MATHEMATICA HUNGARICA | 2004年 / 104卷 / 1-2期

关键词：

bounded variation the seuse of Vitali and of Hardy; multiple Fourier coefficients;

D O I：

10.1023/B:AMHU.0000034364.78876.af

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let f : R-n --> C be a periodic function with period 2pi in each variable and of bounded variation in the sense of Vitali over [0, 2pi](n) with the total variation V(f; [0 2pi](n)). In case f is Lebesgue integrable over the n-dimensional torus [0, 2pi](n) denote by (f) over cap (k(1),..., k(n)) the multiple Fourier coefficients of f, where (k(1),..., k(n)). We present a straightforward proof of the estimate \(f) over cap (k(1),...,k(n))\ less than or equal to V(f; [0, 2pi](n))/(2pi)(n) Pi(j = 1)(n) k(j), provided k(j) not equal 0, j = 1,..., n. Both the order of magnitude and the constant in this estimate are exact.

引用

页码：95 / 104

页数：10

共 9 条

[1] Properties of functions f(x, y) of bounded variation [J].