BOUNDEDNESS OF CALDERON-ZYGMUND OPERATORS ON INHOMOGENEOUS PRODUCT LIPSCHITZ SPACES

In this paper, we study the boundedness of a class of inhomogeneous Journe ''s product singular integral operators on the inhomogeneous product Lipschitz spaces. The consideration of such inhomogeneous Journe ''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.