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http://dx.doi.org/10.4134/JKMS.j210115

BOUNDEDNESS OF CALDERÓN-ZYGMUND OPERATORS ON INHOMOGENEOUS PRODUCT LIPSCHITZ SPACES  

He, Shaoyong (Department of Mathematics Huzhou University)
Zheng, Taotao (Department of Mathematics Zhejiang University of Science and Technology)
Publication Information
Journal of the Korean Mathematical Society / v.59, no.3, 2022 , pp. 469-494 More about this Journal
Abstract
In this paper, we study the boundedness of a class of inhomogeneous Journé's product singular integral operators on the inhomogeneous product Lipschitz spaces. The consideration of such inhomogeneous Journé's product singular integral operators is motivated by the study of the multi-parameter pseudo-differential operators. The key idea used here is to develop the Littlewood-Paley theory for the inhomogeneous product spaces which includes the characterization of a special inhomogeneous product Besov space and a density argument for the inhomogeneous product Lipschitz spaces in the weak sense.
Keywords
Calderon-Zygmund operator; inhomogeneous product Lipschitz space; Littlewood-Paley theory;
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