Second order Riesz transforms associated to the Schrödinger operator for p≤1

Fu Ken Ly

    Research output: Contribution to journalArticlepeer-review

    10 Citations (Scopus)

    Abstract

    Let L=-δ+V be the Schrödinger operator on Rn, where V belongs to the class of reverse Hölder weights RH q for some q>max{2, n/2}. We show that the second order Riesz transforms ∇; 2L -1 and VL -1 are bounded from the Hardy spaces HLp(Rn) associated to L into Lp(Rn) for 0<p≤1. We show also that the operators ∇; 2L -1 map the classical Hardy spaces Hp(Rn) into Hp(Rn) for a restricted range of p.

    Original languageEnglish
    Pages (from-to)391-402
    Number of pages12
    JournalJournal of Mathematical Analysis and Applications
    Volume410
    Issue number1
    DOIs
    Publication statusPublished - 1 Feb 2014

    Keywords

    • Hardy spaces
    • Reverse Hölder
    • Riesz transforms
    • Schrödinger operators

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