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On Boundedness Property of Singular Integral Operators Associated to a Schrödinger Operator in a Generalized Morrey Space and Applications

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Abstract

In this paper, we provide the boundedness property of the Riesz transforms associated to the Schrödinger operator \({\cal L} = \Delta + {\bf{V}}\) in a new weighted Morrey space which is the generalized version of many previous Morrey type spaces. The additional potential V considered in this paper is a non-negative function satisfying the suitable reverse Hölder’s inequality. Our results are new and general in many cases of problems. As an application of the boundedness property of these singular integral operators, we obtain some regularity results of solutions to Schrödinger equations in the new Morrey space.

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Correspondence to Xuan Truong Le or Thanh Nhan Nguyen or Ngoc Trong Nguyen.

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Le, X.T., Nguyen, T.N. & Nguyen, N.T. On Boundedness Property of Singular Integral Operators Associated to a Schrödinger Operator in a Generalized Morrey Space and Applications. Acta Math Sci 40, 1171–1184 (2020). https://doi.org/10.1007/s10473-020-0501-2

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Key words

  • weighted Morrey spaces
  • Schödinger operator
  • riesz transforms
  • Regularity estimates

2010 MR Subject Classification

  • 42B20
  • 42B35