Calderón-Zygmund operators on Lipschitz spaces over RD spaces. Issue 4 (3rd April 2021)

• Record Type: Journal Article
• Authors: Li, Hongliang; Zheng, Taotao
• Is Part Of: Quaestiones mathematicae. Volume 44:Issue 4(2021)
• Page Start: 473
• Page End: 494
• Publication Date: 2021-04-03
• Subjects: 42B20 -- 42B25 -- 46E35; Caldeŕon-Zygmund operators -- spaces of homogeneous type -- RD spaces -- Lip-schitz spaces; Mathematics -- Periodicals; 510.5
• DOI: 10.2989/16073606.2019.1709579
• Languages: English
• ISSNs: 1607-3606

Abstract

Abstract: Suppose that ( X, d, µ ) is a metric measure space of homogeneous type in the sense of Coifman and Weiss with a reverse doubling condition. By establishing the Littlewood-Paley characterization of Lipschitz spaces, a density argument in the weak sense and almost orthogonality estimate we prove that a Caldeŕon-Zygmund operator T is bounded on Lipschitz space if and only if T 1 = 0.