Weighted estimates for powers and smoothing estimates of Schrödinger operators with inverse-square potentials

The Anh Bui*, Piero D'Ancona, Xuan Thinh Duong, Ji Li, Fu Ken Ly

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    5 Citations (Scopus)

    Abstract

    Let La be a Schrödinger operator with inverse square potential a|x|−2 on ℝd, d ≥3. The main aim of this paper is to prove weighted estimates for fractional powers of La. The proof is based on weighted Hardy inequalities and weighted inequalities for square functions associated to La. As an application, we obtain smoothing estimates regarding the propagator eitLa .

    Original languageEnglish
    Pages (from-to)2771-2807
    Number of pages37
    JournalJournal of Differential Equations
    Volume262
    Issue number3
    DOIs
    Publication statusPublished - 2017

    Keywords

    • Inverse-square potential
    • Littlewood–Paley theory
    • Heat kernel estimate
    • Negative power
    • Smoothing estimate

    Fingerprint Dive into the research topics of 'Weighted estimates for powers and smoothing estimates of Schrödinger operators with inverse-square potentials'. Together they form a unique fingerprint.

    Cite this