Arkiv för Matematik

, Volume 44, Issue 2, pp 261–275

Endpoint estimates for Riesz transforms of magnetic Schrödinger operators

Article

DOI: 10.1007/s11512-006-0021-x

Cite this article as:
Duong, X., Ouhabaz, E. & Yan, L. Ark Mat (2006) 44: 261. doi:10.1007/s11512-006-0021-x

Abstract

Let \(A=-(\nabla-i\vec{a})^2+V\) be a magnetic Schrödinger operator acting on L2(Rn), n≥1, where \(\vec{a}=(a_1,\cdots,a_n)\in L^2_{\rm loc}\) and 0≤VL1loc. Following [1], we define, by means of the area integral function, a Hardy space H1A associated with A. We show that Riesz transforms (∂/∂xk-iak)A-1/2 associated with A, \(k=1,\cdots,n\), are bounded from the Hardy space H1A into L1. By interpolation, the Riesz transforms are bounded on Lp for all 1<p≤2.

Copyright information

© Institut Mittag-Leffler 2006

Authors and Affiliations

  • Xuan Thinh Duong
    • 1
  • El Maati Ouhabaz
    • 2
  • Lixin Yan
    • 1
    • 3
  1. 1.Department of MathematicsMacquarie UniversitySydneyAustralia
  2. 2.Laboratoire Bordelais d’Analyse et GeometrieC.N.R.S. UMR 5467 Universite Bordeaux 1TalenceFrance
  3. 3.Department of MathematicsZhongshan UniversityGuangzhouP.R. China