POTENTIAL OPERATORS AND LAPLACE TYPE MULTIPLIERS ASSOCIATED WITH THE TWISTED LAPLACIAN

doi:10.1016/S0252-9602(16)30130-8

Acta mathematica scientia,Series B ›› 2017, Vol. 37 ›› Issue (1): 280-292.doi: 10.1016/S0252-9602(16)30130-8

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POTENTIAL OPERATORS AND LAPLACE TYPE MULTIPLIERS ASSOCIATED WITH THE TWISTED LAPLACIAN

Adam NOWAK¹, Krzysztof STEMPAK²

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.

Abstract

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 L^p-L^q 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 L^p 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

Adam NOWAK, Krzysztof STEMPAK. POTENTIAL OPERATORS AND LAPLACE TYPE MULTIPLIERS ASSOCIATED WITH THE TWISTED LAPLACIAN[J].Acta mathematica scientia,Series B, 2017, 37(1): 280-292.

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POTENTIAL OPERATORS AND LAPLACE TYPE MULTIPLIERS ASSOCIATED WITH THE TWISTED LAPLACIAN

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