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| Restriction Theorems on M\'{e}tiver Groups Associated to Joint Functional Calculus |
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Citation： |
Heping LIU,An ZHANG.Restriction Theorems on M\'{e}tiver Groups Associated to Joint Functional Calculus[J].Chinese Annals of Mathematics B,2018,39(6):1017~1032 |
| Page view： 608
Net amount： 748 |
Authors： |
Heping LIU; An ZHANG |
Foundation： |
This work was supported by the National Natural Science
Foundation of China (No.11371036) and the Specialized Research
Fund for the Doctoral Program of Higher Education of China
(No.2012000110059). |
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| Abstract： |
The authors get on M\'{e}tivier groups the spectral resolution of a
class of operators $m(\mathcal{L}, -\Delta_\fr{z})$, the joint
functional calculus of the sub-Laplacian and Laplacian on the
centre, and then give some restriction theorems together with their
{asymptotic estimates}, asserting the mix-norm boundedness of the
spectral projection operators $\mathcal{P}_{\mu}^{m}$ for two
classes of functions $m(a,b)= (a^\alpha+b^\beta)^\gamma$ or
$(1+a^\alpha+b^\beta)^\gamma$, with $\alpha, \beta>0,\ \gamma\neq0.$ |
Keywords： |
Restriction operator, M'{e}tivier group, Functional calculus |
Classification： |
22E25, 42B10, 47A60 |
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