A functional calculus and restriction theorem on H-type groups

Heping Liu and Manli Song

Vol. 286 (2017), No. 2, 291–305

DOI: 10.2140/pjm.2017.286.291

Abstract

Let $L$ be the sublaplacian and $T$ the partial laplacian with respect to central variables on H-type groups. We investigate a class of invariant differential operators by the joint functional calculus of $L$ and $T$. We establish Stein–Tomas type restriction theorems for these operators. In particular, the asymptotic behaviors of restriction estimates are given.

Keywords

H-type group, scaled special Hermite expansion, joint functional calculus, restriction operator

Mathematical Subject Classification 2010

Primary: 43A65

Secondary: 42B10, 47A60

Milestones

Received: 30 October 2013

Revised: 6 February 2016

Accepted: 22 July 2016

Published: 15 January 2017