Inhomogeneous Lipschitz spaces of variable order and their applications

Abstract

In this article, the authors first give a Littlewood–Paley characterization for inhomogeneous Lipschitz spaces of variable order with the help of inhomogeneous Calderon identity and almost-orthogonality estimates. As applications, the boundedness of inhomogeneous Calderon–Zygmund singular integral operators of order (ϵ,σ) on these spaces has been presented. Finally, we note that a class of pseudodifferential operators Ta∈OpS1,10 are continuous on the inhomogeneous Lipschitz spaces of variable order as a corollary. We may observe that those operators are not, in general, continuous in L2.