Acta mathematica scientia,Series A ›› 2025, Vol. 45 ›› Issue (3): 665-686.

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Plancherel-Pôlya Type Characterization of Product Weighted Besov and Product Weighted Triebel-Lizorkin Spaces Based on Wavelet Basis

Ziyan Li(),Xiangxing Tao*()   

  1. School of Science, Zhejiang University of Science and Technology, Hangzhou 310023
  • Received:2024-05-20 Revised:2025-01-26 Online:2025-06-26 Published:2025-06-20
  • Supported by:
    NSFC(12271483);Postgraduate Research Innovation Fund of Zhejiang University of Science and Technology(2023yjskc23)

Abstract:

On the product spaces of homogeneous type in the sense of Coifman and Weiss, this paper introduces the product weighted Besov space and product weighted Triebel-Lizorkin space based on wavelet basis, and establishes the Plancherel-Pôlya type characterizations of product weighted Besov spaces and product Triebel-Lizorkin spaces via the wavelet reproducing formula and the almost orthogonal estimation, which means that the space are independent of the choice of the orthonormal wavelet basis.

Key words: weighted Besov space, weighted Triebel-Lizorkin space, spaces of homogeneous type, Plancherel-P?lya type characterization

CLC Number: 

  • O174.3
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