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

Yanchang Han, Ji Li, Chaoqiang Tan*

*Corresponding author for this work

    Research output: Contribution to journalArticle

    Abstract

    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 T1 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.

    Original languageEnglish
    Pages (from-to)3580-3598
    Number of pages19
    JournalMathematical Methods in the Applied Sciences
    Volume40
    Issue number10
    DOIs
    Publication statusPublished - 15 Jul 2017

    Keywords

    • Besov spaces
    • Doubling measures
    • Metric spaces
    • Wavelet

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