Semigroup kernels, Poisson bounds, and holomorphic functional calculus

Xuan T. Duong*, Derek W. Robinson

*Corresponding author for this work

    Research output: Contribution to journalArticle

    111 Citations (Scopus)

    Abstract

    Let L be the generator of a continuous holomorphic semigroup S whose action is determined by an integral kernel K on a scale of spaces Lp(X; ρ). Under mild geometric assumptions on (X, ρ), we prove that if L has a bounded H-functional calculus on L2(X; ρ) and K satisfies bounds typical for the Poisson kernel, then L has a bounded H-functional calculus on Lp(X; ρ) for each p ∈.

    Original languageEnglish
    Pages (from-to)89-128
    Number of pages40
    JournalJournal of Functional Analysis
    Volume142
    Issue number1
    DOIs
    Publication statusPublished - 25 Nov 1996

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