Acta mathematica scientia,Series B ›› 2018, Vol. 38 ›› Issue (4): 1214-1226.doi: 10.1016/S0252-9602(18)30809-9

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THE OSCILLATION OF THE POISSON SEMIGROUP ASSOCIATED TO PARABOLIC HERMITE OPERATOR

Ping LI1, Congbian MA2, Youliang HOU3   

  1. 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:2017-01-19 Revised:2017-10-06 Online:2018-08-25 Published:2018-08-25
  • Contact: Ping LI,E-mail:liping@whu.edu.cn E-mail:liping@whu.edu.cn
  • 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.

Key words: oscillation operator, Possion semigroup, parabolic Hermite operator

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