Characterization of Hölder and Sobolev spaces via the continuous wavelet transform with rotations

被引:0
|
作者
Jaime Navarro
机构
[1] Universidad Autonoma Metropolitana,Department of Basic Sciences
来源
Advances in Operator Theory | 2023年 / 8卷
关键词
Admissible function; Continuous wavelet transform with rotations; Hölder and Sobolev spaces; Weak solutions; 42C40; 47A52; 47A67;
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摘要
The continuous wavelet transform with rotations in higher dimensions is used to characterize the Hölder and Sobolev spaces for functions f∈L2(Rn)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f\in L^2({\mathbb {R}}^n)$$\end{document}. Besides we establish the relationship between Hölder continuity and the decay of the continuous wavelet transform with rotations, as well as for the Sobolev spaces.
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