基于小波基的乘积加权 Besov 空间和乘积加权 Triebel-Lizorkin 空间的 Plancherel-Pôlya 型刻画

Abstract

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

Li Ziyan, Tao Xiangxing. Plancherel-Pôlya Type Characterization of Product Weighted Besov and Product Weighted Triebel-Lizorkin Spaces Based on Wavelet Basis[J].Acta mathematica scientia,Series A, 2025, 45(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

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