On characterization of Poisson integrals of Schrödinger operators with BMO traces

Xuan Thinh Duong*, Lixin Yan, Chao Zhang

*Corresponding author for this work

    Research output: Contribution to journalArticle

    14 Citations (Scopus)

    Abstract

    Let L be a Schrödinger operator of the form L=-δ + V acting on L2(Rn) where the nonnegative potential V belongs to the reverse Hölder class Bq for some q≥n. Let BMOL(Rn) denote the BMO space on Rn associated to the Schrödinger operator L. In this article we will show that a function f∈BMOL(Rn) is the trace of the solution of Lu=-utt+Lu=0, u(x, 0)=f(x), where u satisfies a Carleson condition. Conversely, this Carleson condition characterizes all the L-harmonic functions whose traces belong to the space BMOL(Rn). This result extends the analogous characterization founded by Fabes, Johnson and Neri in [13] for the classical BMO space of John and Nirenberg.

    Original languageEnglish
    Pages (from-to)2053-2085
    Number of pages33
    JournalJournal of Functional Analysis
    Volume266
    Issue number4
    DOIs
    Publication statusPublished - 15 Feb 2014

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