Convergence of multi-dimensional integral operators and applications

被引:1
|
作者
Szarvas, Kristof [1 ]
Weisz, Ferenc [1 ]
机构
[1] Eotvos L Univ, Dept Numer Anal, Pazmany P Setany 1-C, H-1117 Budapest, Hungary
关键词
Variable Lebesgue spaces; Multidimensional integral operators; Multidimensional theta-summation; Multidimensional discrete wavelet transform; POINTWISE CONVERGENCE; FOURIER; SUMMABILITY;
D O I
10.1007/s10998-016-0157-9
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper we investigate a general multi-dimensional integral operator . Under the condition that the kernel function of is in a suitable Herz space, we get several convergence theorems about norm and almost everywhere convergence and convergence at Lebesgue points. The multi-dimensional convergence is investigated over cones and cone-like sets. As special cases we consider three multi-dimensional integral operators, the -summation of Fourier transforms and Fourier series and the discrete wavelet transforms. The convergence results are formulated for functions from the Wiener amalgam spaces and variable Lebesgue spaces, too.
引用
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页码:40 / 66
页数:27
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