Acta mathematica scientia,Series B ›› 2026, Vol. 46 ›› Issue (1): 99-111.doi: 10.1007/s10473-026-0106-5

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THE BOUNDEDNESS OF INHOMOGENEOUS CALDERÓN-ZYGMUND CONVOLUTION OPERATORS ON LOCAL PRODUCT HARDY SPACES

Shaoyong HE1,*, Jiecheng CHEN2   

  1. 1. Department of Mathematics, Huzhou University, Huzhou 313000, China;
    2. Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China
  • Received:2024-08-01 Revised:2024-12-09 Online:2026-01-25 Published:2026-05-22
  • Contact: * Shaoyong HE, E-mail: hsyongmath@sina.com
  • About author:Jiecheng CHEN, E-mail: jcchen@zjnu.edu.cn
  • Supported by:
    The first author was supported by the NSFC (12301115) and the Natural Science Foundation of Huzhou (2023YZ11, 2024YZ37), the second author was supported by the NSFC (12071437).

Abstract: It is well known that the inhomogeneous Calderón-Zygmund convolution operators are bounded on the local Hardy spaces. In this paper, we prove that these operators are bounded on the local product Hardy spaces and the Lipschitz spaces. The key ideas used here are the discrete local Calderón identity and a density argument for the inhomogeneous product Lipschitz spaces in the weak sense.

Key words: local Hardy space, Lipschitz space, inhomogeneous Calderón-Zygmund operator, discrete Calderón identity

CLC Number: 

  • 42B20
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