Inhomogeneous Besov spaces associated to operators with off-diagonal semigroup estimates

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    Abstract

    Let (X, d, μ) be a space of homogeneous type equipped with a distance d and a measure μ. Assume that L is a closed linear operator which generates an analytic semigroup e-tL, t > 0. Also assume that L has a bounded H-calculus on L2(X) and satisfies the Lp -Lq semigroup estimates (which is weaker than the pointwise Gaussian or Poisson heat kernel bounds). The aim of this paper is to establish a theory of inhomogeneous Besov spaces associated to such an operator L. We prove the molecular decompositions for the new Besov spaces and obtain the boundedness of the fractional powers (I + L), γ > 0 on these Besov spaces. Finally, we carry out a comparison between our new Besov spaces and the classical Besov spaces.

    Original languageEnglish
    Pages (from-to)191-234
    Number of pages44
    JournalAdvances in Differential Equations
    Volume22
    Issue number3-4
    Publication statusPublished - 2017

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