Annals of Functional Analysis
- Ann. Funct. Anal.
- Volume 9, Number 1 (2018), 72-86.
Inhomogeneous Lipschitz spaces of variable order and their applications
In this article, the authors first give a Littlewood–Paley characterization for inhomogeneous Lipschitz spaces of variable order with the help of inhomogeneous Calderón identity and almost-orthogonality estimates. As applications, the boundedness of inhomogeneous Calderón–Zygmund singular integral operators of order on these spaces has been presented. Finally, we note that a class of pseudodifferential operators 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 .
Ann. Funct. Anal. Volume 9, Number 1 (2018), 72-86.
Received: 16 October 2016
Accepted: 20 February 2017
First available in Project Euclid: 29 June 2017
Permanent link to this document
Digital Object Identifier
Primary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.)
Secondary: 42B25: Maximal functions, Littlewood-Paley theory 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems
Tan, Jian; Zhao, Jiman. Inhomogeneous Lipschitz spaces of variable order and their applications. Ann. Funct. Anal. 9 (2018), no. 1, 72--86. doi:10.1215/20088752-2017-0025. https://projecteuclid.org/euclid.afa/1498723215