Riesz transforms associated to Schrödinger operators on weighted Hardy spaces

Liang Song*, Lixin Yan

*Corresponding author for this work

    Research output: Contribution to journalArticle

    34 Citations (Scopus)

    Abstract

    Let w be some Ap weight and enjoy reverse Hölder inequality, and let L=-Δ+V be a Schrödinger operator on Rn, where V?Lloc1(Rn) is a non-negative function on Rn. In this article we introduce weighted Hardy spaces HL,w1(Rn) associated to L in terms of the area function characterization, and prove their atomic characters. We show that the Riesz transform ?L?1/2 associated to L is bounded on Lwp(Rn) for 1<p<2, and bounded from HL,w1(Rn) to the classical weighted Hardy space Hw1(Rn).

    Original languageEnglish
    Pages (from-to)1466-1490
    Number of pages25
    JournalJournal of Functional Analysis
    Volume259
    Issue number6
    DOIs
    Publication statusPublished - Sep 2010

    Keywords

    • Atom
    • Heat semigroup
    • Molecule
    • Riesz transform
    • Schrödinger operator
    • Weighted Hardy space

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