 

Taotao Zheng and
Xiangxing Tao
Tb theorem for the generalized singular integral operator on product Lipschitz spaces with paraaccretive functions
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Published: 
September 16, 2020. 
Keywords: 
Product homogeneous Lipschitz spaces, LittlewoodPaley theory, generalized singular integral operator, Besov spaces, paraaccretive function. 
Subject: 
Primary 42B20; Secondary 42B25. 


Abstract
By developing the LittlewoodPaley characterization for product homogeneous Lipschitz spaces
Lip(α_{1},α_{2})(R^{n} × R^{m}) and
Lip_{b}(α_{1},α_{2})(R^{n} × R^{m}), and establishing a density argument for Lip_{b}(α_{1},α_{2})(R^{n} × R^{m}) in the weak sense, we give a Tb theorem for the generalized singular integral operator on
Lip_{b}(α_{1},α_{2})(R^{n} × R^{m}), where
b(x,y) = b_{1}(x)b_{2}(y), b_{1}, b_{2} are paraaccretive functions on
R^{n} and R^{m}, 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

