Riesz transforms in the absence of a preservation condition, with applications to the Dirichlet Laplacian

Joshua Peate

    Research output: Contribution to journalArticlepeer-review

    Abstract

    Let L be a linear operator defined such that −L generates an associated heat semigroup e−tL. Suppose this semigroup does not satisfy a preservation condition. A proof that a generalised Riesz transform Dg(L) satisfies Lp bounds for some range 2<p<q is provided based on two new estimates. One is a Hardy type inequality for L, the other a bound regarding how the gradient of the heat semigroup acts on a characteristic function. Applications are to cases where L is the Dirichlet Laplacian ΔΩ on inner uniform subsets of Rn.

    Original languageEnglish
    Pages (from-to)425-457
    Number of pages33
    JournalJournal of Mathematical Analysis and Applications
    Volume460
    Issue number1
    DOIs
    Publication statusPublished - 1 Apr 2018

    Keywords

    • Dirichlet Laplacian
    • Harmonic analysis
    • Riesz transforms

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