Strong Cesaro summability of double Fourier integrals

被引：3
|
作者：
Brown, G. [1 ]
Feng, D.
Moricz, F.
机构：
[1] Univ Sydney, Sydney, NSW 2006, Australia
[2] Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada
[3] Univ Szeged, Bolyai Inst, H-6720 Szeged, Hungary
来源：
ACTA MATHEMATICA HUNGARICA | 2007年 / 115卷 / 1-2期
基金：
匈牙利科学研究基金会; 中国国家自然科学基金; 澳大利亚研究理事会;
关键词：
double Fourier transform and integral; inversion formula; partial (or Dirichlet) integral; summability; (C; 1); strong q-Cesaro summability;
D O I：
10.1007/s10474-007-4185-z
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove the following theorem. Assume f is an element of L-infinity (R-2) with bounded support. If f is continuous at some point (x(1); x(2)) is an element of R-2, then the double Fourier integral of f is strongly q-Cesaro summable at (x(1); x(2)) to the function value f (x(1); x(2)) for every 0 < q < infinity. Furthermore, if f is continuous on some open subset G of R-2, then the strong q-Cesaro summability of the double Fourier integral of f is locally uniform on G.
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页码：1 / 12
页数：12
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