Stability of integral operators on a space of homogeneous type. Issue 2 (2nd June 2016)

• Record Type: Journal Article
• Authors: Fang, Qiquan; Eon Shin, Chang
• Is Part Of: Mathematische Nachrichten. Volume 290:Issue 2/3(2017)
• Page Start: 284
• Page End: 292
• Publication Date: 2016-06-02
• Subjects: Stability -- integral operators -- spaces of homogeneous type -- 31B10 -- 45P05 -- 46E30 -- 47B38 -- 47G10; Mathematics -- Periodicals; 510.5
• DOI: 10.1002/mana.201500389
• Languages: English
• ISSNs: 0025-584X

Abstract

Abstract : In this paper, we consider integral operators T on compact spaces of homogeneous type with finite diameter, whose kernels K T have certain Hölder regularity and mild singularity near the diagonal. We show that given any z ≠ 0, the L p ‐stability of the operator z I − T is equivalent for different 1 ≤ p ≤ ∞, where I stands for the identity operator.