Besov spaces associated with operators

Anthony Wong

    Research output: Contribution to journalArticle

    Abstract

    Recent work of Bui, Duong and Yan in [2] defined Besov spaces associated with a certain operator L under the weak assumption that L generates an analytic semigroup e-tL with Poisson kernel bounds on L²(X) where X is a (possibly non-doubling) quasimetric space of polynomial upper bound on volume growth. This note aims to extend certain results in [2] to a more general setting when the underlying space can have different dimensions at 0 and infinity. For example, we make some extensions to the Besov norm equivalence result in Proposition 4.4 of [2], such as to more general class of functions with suitable decay at 0 and infinity, and to non-integer k ≥ 1.
    Original languageEnglish
    Pages (from-to)89-104
    Number of pages16
    JournalCommunications in Mathematical Analysis
    Volume16
    Issue number2
    Publication statusPublished - 2014

    Keywords

    • Analytic semigroup
    • Besov space
    • Embedding theorem
    • Heat kernel

    Fingerprint Dive into the research topics of 'Besov spaces associated with operators'. Together they form a unique fingerprint.

    Cite this