On the rate of pointwise divergence of Fourier and wavelet series in Lp

被引：9
|
作者：
Aubry, JM [1 ]
机构：
[1] Univ Paris 12, CNRS, UMR 8050, Lab Anal & Math Appl, F-94010 Creteil, France
来源：
JOURNAL OF APPROXIMATION THEORY | 2006年 / 138卷 / 01期
关键词：
Fourier series; wavelet series; pointwise divergence; Carleson-Hunt theorem; Hausdorff dimension;
D O I：
10.1016/j.jat.2005.10.003
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let g is an element of L-p(T), 1 < p < infinity. We show that the set of points where the Fourier partial sums S(n)g(x) diverge as fast as n(beta) has Hausdorff dimension less or equal to 1 - beta p. A comparable result holds for wavelet series. Conversely, we show that this inequality is sharp and depends only on the Hausdorff dimension of the set of divergence. (c) 2005 Elsevier Inc. All rights reserved.
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页码：97 / 111
页数：15
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