Mathematical Research Letters
Volume 23 (2016)
Boundedness of composition operators associated with mixed homogeneities on Lipschitz spaces
Pages: 1387 – 1403
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].
Lipschitz spaces, singular integral operator, composition operator, isotropic homogeneity, non-isotropic homogeneity, Littlewood–Paley theory
2010 Mathematics Subject Classification
Primary 42B20. Secondary 42B25, 46A35.
Accepted 6 June 2015
Published 12 January 2017