Besov spaces via wavelets on metric spaces endowed with doubling measure, singular integral, and the T1 type theorem | Zendy

Han Yanchang | Zendy; Li Ji | Zendy; Tan Chaoqiang | Zendy

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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.

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