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Besov spaces via wavelets on metric spaces endowed with doubling measure, singular integral, and the T1 type theorem
Author(s) -
Han Yanchang,
Li Ji,
Tan Chaoqiang
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4247
Subject(s) - mathematics , orthonormal basis , lipschitz continuity , besov space , pure mathematics , birnbaum–orlicz space , metric space , measure (data warehouse) , interpolation space , lp space , type (biology) , wavelet , topological tensor product , fréchet space , class (philosophy) , mathematical analysis , discrete mathematics , functional analysis , banach space , ecology , biochemistry , chemistry , physics , quantum mechanics , database , artificial intelligence , biology , computer science , gene
The aim of this paper is twofold. We first establish the Besov spaces on metric spaces endowed with a doubling measure, via the remarkable orthonormal wavelet basis constructed recently by T. Hytönen and O. Tapiola, and characterize the dual spaces of these Besov spaces. Second, we prove the T 1 type theorem for the boundedness of Calderón–Zygmund operators on these Besov spaces. Finally, we introduce a new class of Lipschitz spaces and characterize these spaces via the Littlewood–Paley theory. Copyright © 2016 John Wiley & Sons, Ltd.