Pointwise Convergence of the Calderón Reproducing Formula

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• 作者：Kangwei Li (1) likangwei9@mail.nankai.edu.cn
  Wenchang Sun (1) sunwch@nankai.edu.cn
• 关键词：Calderón reproducing formula – Wavelet transforms – Pointwise convergence
• 刊名：Journal of Fourier Analysis and Applications
• 出版年：2012
• 出版时间：June 2012
• 年：2012
• 卷：18
• 期：3
• 页码：439-455
• 全文大小：422.5 KB
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• 作者单位：1. Department of Mathematics and LPMC, Nankai University, Tianjin, 300071 China
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Fourier Analysis
  Abstract Harmonic Analysis
  Approximations and Expansions
  Partial Differential Equations
  Applications of Mathematics
  Signal,Image and Speech Processing
  
• 出版者：Birkh盲user Boston
• ISSN：1531-5851

文摘

In this paper, we study the pointwise convergence of the Calderón reproducing formula, which is also known as an inversion formula for wavelet transforms. We show that for every f ? L_wp(\mathbb Rd)f\in L_{w}^{p}(\mathbb {R}^{d}) with an A_p\mathcal{A}_{p} weight w, 1≤p<∞, the integral is convergent at every Lebesgue point of f, and therefore almost everywhere. Moreover, we prove the convergence without any assumption on the smoothness of wavelet functions.