Calderón–Zygmund Operators on Homogeneous Product Lipschitz Spaces

Calderón–Zygmund Operators on Homogeneous Product Lipschitz Spaces

The purpose of this paper is to establish a necessary and sufficient condition for the boundedness of product Calderón–Zygmund singular integral operators introduced by Journé on the product Lipschitz spaces. The key idea used in this paper is to develop the Littlewood–Paley theory for the product s...

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Veröffentlicht in:The Journal of Geometric Analysis 2021-02, Vol.31 (2), p.2033-2057
Hauptverfasser: Zheng, Taotao, Chen, Jiecheng, Dai, Jiawei, He, Shaoyong, Tao, Xiangxing
Format: Artikel
Sprache:eng
Schlagworte:
Abstract Harmonic Analysis
Convex and Discrete Geometry
Differential Geometry
Dynamical Systems and Ergodic Theory
Fourier Analysis
Function space
Geometry
Global Analysis and Analysis on Manifolds
Mathematics
Mathematics and Statistics
Operators (mathematics)
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Zusammenfassung:The purpose of this paper is to establish a necessary and sufficient condition for the boundedness of product Calderón–Zygmund singular integral operators introduced by Journé on the product Lipschitz spaces. The key idea used in this paper is to develop the Littlewood–Paley theory for the product spaces which includes the characterization of a special product Besov space and a density argument for the product Lipschitz spaces in the weak sense.
ISSN:1050-6926
1559-002X
DOI:10.1007/s12220-019-00331-y