#### Vol. 286, No. 2, 2017

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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