## Annals of Functional Analysis

### Inhomogeneous Lipschitz spaces of variable order and their applications

#### 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 $(\epsilon,\sigma)$ on these spaces has been presented. Finally, we note that a class of pseudodifferential operators $T_{a}\in\mathcal{O}pS_{1,1}^{0}$ 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 $L^{2}$.

#### Article information

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

Dates
Accepted: 20 February 2017
First available in Project Euclid: 29 June 2017

https://projecteuclid.org/euclid.afa/1498723215

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

#### 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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