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February 2018 Inhomogeneous Lipschitz spaces of variable order and their applications
Jian Tan, Jiman Zhao
Ann. Funct. Anal. 9(1): 72-86 (February 2018). DOI: 10.1215/20088752-2017-0025

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.

Citation

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Jian Tan. Jiman Zhao. "Inhomogeneous Lipschitz spaces of variable order and their applications." Ann. Funct. Anal. 9 (1) 72 - 86, February 2018. https://doi.org/10.1215/20088752-2017-0025

Information

Received: 16 October 2016; Accepted: 20 February 2017; Published: February 2018
First available in Project Euclid: 29 June 2017

zbMATH: 1383.42015
MathSciNet: MR3758744
Digital Object Identifier: 10.1215/20088752-2017-0025

Subjects:
Primary: 42B20
Secondary: 42B25 , 46E35

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

Rights: Copyright © 2018 Tusi Mathematical Research Group

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Vol.9 • No. 1 • February 2018
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