THE OSCILLATION OF THE POISSON SEMIGROUP ASSOCIATED TO PARABOLIC HERMITE OPERATOR

doi:10.1016/S0252-9602(18)30809-9

数学物理学报(英文版) ›› 2018, Vol. 38 ›› Issue (4): 1214-1226.doi: 10.1016/S0252-9602(18)30809-9

THE OSCILLATION OF THE POISSON SEMIGROUP ASSOCIATED TO PARABOLIC HERMITE OPERATOR

李平¹, 马聪变², 侯友良³

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

收稿日期:2017-01-19 修回日期:2017-10-06 出版日期:2018-08-25 发布日期:2018-08-25
通讯作者: Ping LI,E-mail:liping@whu.edu.cn E-mail:liping@whu.edu.cn
作者简介:Congbian MA,E-mail:macongbian@126.com;Youliang HOU,E-mail:ylhou323@whu.edu.cn
基金资助:
This work was supported by National Natural Science Foundation of China (11471251 and 11671308).

THE OSCILLATION OF THE POISSON SEMIGROUP ASSOCIATED TO PARABOLIC HERMITE OPERATOR

Ping LI¹, Congbian MA², Youliang HOU³

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).

摘要/Abstract

摘要：

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

关键词: oscillation operator, Possion semigroup, parabolic Hermite operator

Abstract:

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

李平, 马聪变, 侯友良. THE OSCILLATION OF THE POISSON SEMIGROUP ASSOCIATED TO PARABOLIC HERMITE OPERATOR[J]. 数学物理学报(英文版), 2018, 38(4): 1214-1226.

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.

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THE OSCILLATION OF THE POISSON SEMIGROUP ASSOCIATED TO PARABOLIC HERMITE OPERATOR

THE OSCILLATION OF THE POISSON SEMIGROUP ASSOCIATED TO PARABOLIC HERMITE OPERATOR

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