Old and new Morrey spaces with heat Kernel bounds

Xuan Thinh Duong*, Jie Xiao, Lixin Yan

*Corresponding author for this work

    Research output: Contribution to journalArticle

    70 Citations (Scopus)

    Abstract

    Given p ∈ [1,∞) and λ (0, n), we study Morrey space Lp,λ(ℝn) of all locally integrable complex-valued functions f on ℝn such that for every open Euclidean ball B ⊂ ℝn with radius rB there are numbers C = C(f ) (depending on f ) and c = c(f, B) (relying upon f and B) satisfying rBB |f(x) - c| p dx ≤ C and derive old and new, two essentially different cases arising from either choosing c = fB = |B|-1B f(y)dy or replacing c by PtB (x) = ∫tB ptB (x, y)f (y)dy-where tB is scaled to rB and pt(•, •) is the kernel of the infinitesimal generator L of an analytic semigroup {e-tL} t≥0 on L2(ℝn). Consequently, we are led to simultaneously characterize the old and new Morrey spaces, but also to show that for a suitable operator L, the new Morrey space is equivalent to the old one.

    Original languageEnglish
    Pages (from-to)87-111
    Number of pages25
    JournalJournal of Fourier Analysis and Applications
    Volume13
    Issue number1
    DOIs
    Publication statusPublished - Feb 2007

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