Vol. 286, No. 2, 2017

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ISSN: 0030-8730
A functional calculus and restriction theorem on H-type groups

Heping Liu and Manli Song

Vol. 286 (2017), No. 2, 291–305
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
Authors
Heping Liu
LMAM, School of Mathematical Sciences
Peking University
Beijing, 100871
China
Manli Song
School of Natural and Applied Sciences
Northwestern Polytechnical University
Xi’an, 710129
China