Acta mathematica scientia,Series A ›› 2011, Vol. 31 ›› Issue (3): 611-619.

• Articles • Previous Articles     Next Articles

An Estimate for the Schr¨odinger Type Operators with Certain Nonnegative Potentials

 LIU Yu   

  1. Department of Mathematics and Mechanics, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083
  • Received:2009-08-22 Revised:2010-08-19 Online:2011-06-25 Published:2011-06-25
  • Supported by:

    国家自然科学基金(10901018) 和北京科技大学冶金工程研究院理论研究基金(00009503)资助

Abstract:

Let L = −Δ+ V be the Schr¨odinger operator on Rd with the potential V being a nonnegative polynomial. BMOL(Rd) is a dual space of the Hardy-type space H1 L(Rd) related to Schr¨odinger operator L = −Δ+V . In this article it is proved that the Schr¨odinger type operator (−Δ+ V )β is bounded from Lp(Rd) into BMOL(Rd) for p = d/2β−1 when the potential V is a nonnegative polynomial.

Key words: BMOL(Rd), Schr¨odinger operators, Reverse Hölder class

CLC Number: 

  • 35J10
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