Stability of Localized Integral Operators on Normal Spaces of Homogeneous Type. (4th April 2019)

• Record Type: Journal Article
• Authors: Fang, Qiquan; Shin, Chang Eon
• Is Part Of: Numerical functional analysis and optimization. Volume 40:Number 5(2019)
• Page Start: 491
• Page End: 512
• Publication Date: 2019-04-04
• Subjects: Localized integral operators -- spaces of homogeneous type -- stability -- 2010; 47G10 -- 45P05 -- 47B38 -- 31B10 -- 46E30; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2018.1560316
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: The L p -stability of linear operators is one of fundamental concepts in many research fields. In this article, we introduce a family of localized integral operators on a normal space of homogeneous type such that their kernels have some off-diagonal decay, mild singularity near the diagonal and certain Hölder regularity, and we show that localized integral operators in the family have their L p -stability to be equivalent for different exponents 1 ≤ p ≤ ∞ .