Endpoint estimates for commutators of singular integrals related to Schrödinger operators

  • Luong Dang Ky

    University of Quy Nhon, Quy Nhon, Binh Dinh, Vietnam

Abstract

Let be a Schrödinger operator on , , where is a nonnegative potential, , and belongs to the reverse H\"older class . In this paper, we study the commutators for in a class of sublinear operators containing the fundamental operators in harmonic analysis related to . More precisely, when , we prove that there exists a bounded subbilinear operator such that

where is a bounded bilinear operator from into which does not depend on . The subbilinear decomposition allows us to explain why commutators with the fundamental operators are of weak type , and when a commutator is of strong type .

Also, we discuss the -estimates for commutators of the Riesz transforms associated with the Schrödinger operator .

Cite this article

Luong Dang Ky, Endpoint estimates for commutators of singular integrals related to Schrödinger operators. Rev. Mat. Iberoam. 31 (2015), no. 4, pp. 1333–1373

DOI 10.4171/RMI/871