Inhomogeneous multi-parameter Lipschitz spaces associated with different homogeneities and their applications

Abstract

This paper is motivated by Phong and Stein's work in \cite{ps}. The purpose of this paper is to establish the inhomogeneous multi-parameter
Lipschitz spaces~${Lip}_{com}^\alpha$
associated with mixed homogeneities
and characterize these spaces via the Littlewood-Paley theory.
As applications, the boundedness of the composition of
Calder\'on-Zygmund singular integral operators
with mixed homogeneities
has been considered.