Convergence of multi-dimensional integral operators and applications

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• 作者：Kristóf Szarvas ; Ferenc Weisz
• 关键词：Variable Lebesgue spaces ; Multidimensional integral operators ; Multidimensional \(\theta \) ; summation ; Multidimensional discrete wavelet transform
• 刊名：Periodica Mathematica Hungarica
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：74
• 期：1
• 页码：40-66
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general;
• 出版者：Springer Netherlands
• ISSN：1588-2829
• 卷排序：74

文摘

In this paper we investigate a general multi-dimensional integral operator \(V_{T}\). Under the condition that the kernel function of \(V_{T}\) 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 \(\theta \)-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.