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New York Journal of Mathematics
Volume 26 (2020), 1028-1063

  

Taotao Zheng and Xiangxing Tao

Tb theorem for the generalized singular integral operator on product Lipschitz spaces with para-accretive functions

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Published: September 16, 2020.
Keywords: Product homogeneous Lipschitz spaces, Littlewood-Paley theory, generalized singular integral operator, Besov spaces, para-accretive function.
Subject: Primary 42B20; Secondary 42B25.

Abstract
By developing the Littlewood-Paley characterization for product homogeneous Lipschitz spaces Lip(α12)(Rn × Rm) and Lipb12)(Rn × Rm), and establishing a density argument for Lipb12)(Rn × Rm) in the weak sense, we give a Tb theorem for the generalized singular integral operator on Lipb12)(Rn × Rm), where b(x,y) = b1(x)b2(y), b1, b2 are para-accretive functions on Rn and Rm, respectively.

Acknowledgements

This research was supported by National Natural Science Foundation of China (Grant No. 11626213, 11771399, 11671357) and Zhejiang Provincial Natural Science Foundation of China (Grant No. LQ17A010002).


Author information

Taotao Zheng:
Department of Mathematics
Zhejiang University of Science and Technology
Hangzhou, Zhejiang 310023, China

zhengtao@zust.edu.cn

Xiangxing Tao:
Department of Mathematics
Zhejiang University of Science and Technology
Hangzhou, Zhejiang 310023, China

xxtao@zust.edu.cn