数学物理学报(英文版) ›› 2017, Vol. 37 ›› Issue (1): 280-292.doi: 10.1016/S0252-9602(16)30130-8

• 论文 • 上一篇    

POTENTIAL OPERATORS AND LAPLACE TYPE MULTIPLIERS ASSOCIATED WITH THE TWISTED LAPLACIAN

Adam NOWAK1, Krzysztof STEMPAK2   

  1. 1. Instytut Matematyczny, Polska Akademia Nauk, sniadeckich 8, 00-656 Warszawa, Poland;
    2. Wydzial Matematyki, Politechnika Wroc lawska, Wyb. Wyspianskiego 27, 50-370 Wroc law, Poland
  • 收稿日期:2015-08-27 修回日期:2016-04-11 出版日期:2017-02-25 发布日期:2017-02-25
  • 作者简介:Adam NOWAK,E-mail:adam.nowak@impan.pl;Krzysztof STEMPAK,E-mail:krzysztof.stempak@pwr.edu.pl
  • 基金资助:

    This research was supported by the National Science Centre of Poland within the project Opus 2013/09/B/ST1/02057.

POTENTIAL OPERATORS AND LAPLACE TYPE MULTIPLIERS ASSOCIATED WITH THE TWISTED LAPLACIAN

Adam NOWAK1, Krzysztof STEMPAK2   

  1. 1. Instytut Matematyczny, Polska Akademia Nauk, sniadeckich 8, 00-656 Warszawa, Poland;
    2. Wydzial Matematyki, Politechnika Wroc lawska, Wyb. Wyspianskiego 27, 50-370 Wroc law, Poland
  • Received:2015-08-27 Revised:2016-04-11 Online:2017-02-25 Published:2017-02-25
  • About author:Adam NOWAK,E-mail:adam.nowak@impan.pl;Krzysztof STEMPAK,E-mail:krzysztof.stempak@pwr.edu.pl
  • Supported by:

    This research was supported by the National Science Centre of Poland within the project Opus 2013/09/B/ST1/02057.

摘要:

We study potential operators and, more generally, Laplace-Stieltjes and Laplace type multipliers associated with the twisted Laplacian. We characterize those 1≤p, q≤∞, for which the potential operators are Lp-Lq bounded. This result is a sharp analogue of the classical Hardy-Littlewood-Sobolev fractional integration theorem in the context of special Hermite expansions. We also investigate Lp mapping properties of the Laplace-Stieltjes and Laplace type multipliers.

关键词: twisted Laplacian, special Hermite expansion, negative power, potential operator, fractional integral, potential kernel, spectral multiplier, singular oscillatory integral

Abstract:

We study potential operators and, more generally, Laplace-Stieltjes and Laplace type multipliers associated with the twisted Laplacian. We characterize those 1≤p, q≤∞, for which the potential operators are Lp-Lq bounded. This result is a sharp analogue of the classical Hardy-Littlewood-Sobolev fractional integration theorem in the context of special Hermite expansions. We also investigate Lp mapping properties of the Laplace-Stieltjes and Laplace type multipliers.

Key words: twisted Laplacian, special Hermite expansion, negative power, potential operator, fractional integral, potential kernel, spectral multiplier, singular oscillatory integral