Annals of Functional Analysis

Inhomogeneous Lipschitz spaces of variable order and their applications

Jian Tan and Jiman Zhao

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Abstract

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 (ϵ,σ) on these spaces has been presented. Finally, we note that a class of pseudodifferential operators TaOpS1,10 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.

Article information

Source
Ann. Funct. Anal. Volume 9, Number 1 (2018), 72-86.

Dates
Received: 16 October 2016
Accepted: 20 February 2017
First available in Project Euclid: 29 June 2017

Permanent link to this document
https://projecteuclid.org/euclid.afa/1498723215

Digital Object Identifier
doi:10.1215/20088752-2017-0025

Subjects
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

Keywords
inhomogeneous Lipschitz space variable exponent almost-orthogonal estimate Littlewood–Paley theory pseudodifferential operator

Citation

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


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