Absolute convergence of double series of Fourier-Haar coefficients for functions of bounded p-variation

被引：7
作者：
B. I. Golubov
机构：
[1] Moscow Institute of Physical Technologies, State University, Dolgoprudnyi, Moscow Region, 141700
来源：
Russian Mathematics | 2012年 / 56卷 / 6期
基金：
俄罗斯基础研究基金会;
关键词：
Double Haar system; Fourier-Haar coefficients; Functions of two variables of bounded p-variation;
D O I：
10.3103/S1066369X12060011
中图分类号：
学科分类号：
摘要：
We consider functions of two variables of bounded p-variation of the Hardy type on the unit square. For these functions we obtain a sufficient condition for the absolute convergence of series of positive powers of Fourier coefficients with power-type weights with respect to the double Haar system. This condition implies those for the absolute convergence of series of Fourier-Haar coefficients of one-variable functions which have a bounded Wiener p-variation or belong to the class Lip a. We show that the obtained results are unimprovable. We also formulate N-dimensional analogs of the main result and its corollaries. © Allerton Press, Inc., 2012.
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页码：1 / 10
页数：9
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