Boundedness of composition operators associated with mixed homogeneities on Lipschitz spaces

Yanchang Han, Yongsheng Han
2016 Mathematical Research Letters  
This note is motivated by Phong and Stein's work in [PS]. We introduce a new class of Lipschitz spaces associated with mixed homogeneities and characterize these spaces via the Littlewood-Paley theory. We prove that the composition of two Calderón-Zygmund singular integral operators with different homogeneities is bounded on these Lipschitz spaces. Our result answers a question arises in the context of Lipschitz spaces due to the constructions in [MR].
doi:10.4310/mrl.2016.v23.n5.a7 fatcat:jibhooxysncbza7sen4x4opdiq