Boundedness of singular integrals and their commutators with BMO functions on hardy spaces

Anh Bui*, Xuan Thinh Duong

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    6 Citations (Scopus)

    Abstract

    In this paper, we establish suffcient conditions for a singular integral T to be bounded from certain Hardy spaces Hp L to Lebesgue spaces Lp, 0 < p (≤ 1, and for the commutator of T and a BMO function to be weak-type bounded on Hardy space H(1 L. We then show that our suffcient conditions are applicable to the following cases: (i) T is the Riesz transform or a square function associated with the Laplace- Beltrami operator on a doubling Riemannian manifold, (ii) T is the Riesz transform associated with the magnetic Schrödinger operator on a Euclidean space, and (iii) T = g(L) is a singular integral operator deffned from the holomorphic functional calculus of an operator L or the spectral multiplier of a non-negative self-adjoint operator L.

    Original languageEnglish
    Pages (from-to)459-494
    Number of pages36
    JournalAdvances in Differential Equations
    Volume18
    Issue number5-6
    Publication statusPublished - 2013

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