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Stability of integral operators on a space of homogeneous type
Author(s) -
Fang Qiquan,
Shin Chang
Publication year - 2017
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201500389
Subject(s) - mathematics , homogeneous , diagonal , operator (biology) , type (biology) , fourier integral operator , mathematical analysis , pure mathematics , stability (learning theory) , singularity , operator theory , singular integral operators , space (punctuation) , identity (music) , combinatorics , geometry , philosophy , repressor , ecology , linguistics , chemistry , computer science , acoustics , biology , biochemistry , machine learning , transcription factor , physics , gene
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.