L p estimates for the Schrödinger type operators

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Abstract

Let L k = (−Δ) k + V k be a Schrödinger type operator, where k ≥ 1 is a positive integer and V is a nonnegative polynomial. We obtain the L p estimates for the operators ∇2k L k −1 and ∇ k L k −1/2 .

Keywords

Lp estimate reverse Hölder class Schrödinger operator 

MR Subject Classification

35J10 42B20 
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Copyright information

© Editorial Committee of Applied Mathematics-A Journal of Chinese Universities and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.School of Mathematics and PhysicsUniversity of Science and Technology BeijingBeijingChina
  2. 2.College of SciencesNorth China University of TechnologyBeijingChina

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