Commutators of Riesz transforms of magnetic Schrödinger operators

Xuan Thinh Duong, Lixin Yan

    Research output: Contribution to journalArticle

    12 Citations (Scopus)

    Abstract

    Let A = -(∇ - ia)·(∇ - ia ) + V be a magnetic Schrödinger operator acting on L 2(ℝn), n ≥ 1, where a = (a 1,...,an) ∈ Lloc 2 (ℝn, ℝn) and 0 ≤ V ∈ L loc 1(ℝn). In this paper, we show that when a function b ∈ BMO(ℝn), the commutators [b, T k]f = Tk(bf) - bTk f, k = 1,..., n, are bounded on Lp(ℝn) for all 1 < p < 2, where the operators Tk are Riesz transforms (∂/∂xk - iak)A-1/2 associated with A.

    Original languageEnglish
    Pages (from-to)219-234
    Number of pages16
    JournalManuscripta Mathematica
    Volume127
    Issue number2
    DOIs
    Publication statusPublished - Oct 2008

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