Endpoint boundedness of commutators on spaces of homogeneous type. Issue 14 (26th October 2017)

• Record Type: Journal Article
• Authors: Liu, Liguang; Chang, Der-Chen; Fu, Xing; Yang, Dachun
• Is Part Of: Applicable analysis. Volume 96:Issue 14(2017)
• Page Start: 2408
• Page End: 2433
• Publication Date: 2017-10-26
• Subjects: Space of homogeneous type -- bilinear decomposition -- commutator -- Calderón–Zygmund operator -- Hardy space -- BMO; Primary: 47B47 -- Secondary: 42B20 -- 42B30 -- 42C40 -- 30L99; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2017.1341628
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract: Let be a space of homogeneous type in the sense of Coifman and Weiss. Let be a family of sublinear operators that include the well-known Calderón–Zygmund operator. The authors prove that the commutator [ b, T ] is bounded from a Hardy-type subspace of to, where denotes the Lebesgue space of all integrable functions, the atomic Hardy space of Coifman and Weiss with the dual space, b is a non-constant -function and . Indeed, the space is the largest subspace in that possesses this property. The approach taken in this article adopts the bilinear decomposition theory for the product of functions in and .