Article

Arkiv för Matematik

, Volume 44, Issue 2, pp 261-275

Endpoint estimates for Riesz transforms of magnetic Schrödinger operators

  • Xuan Thinh DuongAffiliated withDepartment of Mathematics, Macquarie University Email author 
  • , El Maati OuhabazAffiliated withLaboratoire Bordelais d’Analyse et Geometrie, C.N.R.S. UMR 5467 Universite Bordeaux 1
  • , Lixin YanAffiliated withDepartment of Mathematics, Macquarie UniversityDepartment of Mathematics, Zhongshan University

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Abstract

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