Potential operators and laplace type multipliers associated with the twisted laplacian

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• 作者：Adam NOWAK ^{adam.nowak@impan.pl}
• 关键词：twisted Laplacian ; special Hermite expansion ; negative power ; potential operator ; fractional integral ; potential kernel ; spectral multiplier ; singular oscillatory integral
• 刊名：Acta Mathematica Scientia
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：37
• 期：1
• 页码：280-292
• 全文大小：270 K
• 卷排序：37

文摘

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.