Articles

THE OSCILLATION OF THE POISSON SEMIGROUP ASSOCIATED TO PARABOLIC HERMITE OPERATOR

  • Ping LI ,
  • Congbian MA ,
  • Youliang HOU
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  • 1. School of Information and Mathematics, Yangze University, Jingzhou 434023, China;
    2. School of Mathematics and Information Science, Xinxiang University, Xinxiang 453002, China;
    3. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

Received date: 2017-01-19

  Revised date: 2017-10-06

  Online published: 2018-08-25

Supported by

This work was supported by National Natural Science Foundation of China (11471251 and 11671308).

Abstract

Let O(PτL) be the oscillation of the Possion semigroup associated with the parabolic Hermite operator L=t-△+|x|2. We show that O(PτL) is bounded from Lp(Rn+1) into itself for 1 < p < ∞, bounded from L1(Rn+1) into weak-L1(Rn+1) and bounded from Lc (Rn+1) into BMO(Rn+1). In the case p=∞ we show that the range of the image of the operator O(PτL) is strictly smaller than the range of a general singular operator.

Cite this article

Ping LI , Congbian MA , Youliang HOU . THE OSCILLATION OF THE POISSON SEMIGROUP ASSOCIATED TO PARABOLIC HERMITE OPERATOR[J]. Acta mathematica scientia, Series B, 2018 , 38(4) : 1214 -1226 . DOI: 10.1016/S0252-9602(18)30809-9

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