Abstract
The purpose of this paper is to establish a necessary and sufficient condition for the boundedness of product Calderon–Zygmund singular integral operators introduced by Journe 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.
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