Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A multiplier theorem for $ SU(n)$

Author: Norman J. Weiss
Journal: Proc. Amer. Math. Soc. 59 (1976), 366-370
MSC: Primary 43A22; Secondary 22E30
MathSciNet review: 0420141
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Abstract: Let $ G = {\text{SU}}(n)$, let $ \mathfrak{g}$ be its Lie algebra and let $ m$ be a function on $ \mathfrak{g}$, invariant under the adjoint action of $ G$, which is continuous at the points of $ \hat G$ (which can be imbedded in $ \mathfrak{g}$). If $ 1 \leqslant p < 2[1 - {(n + 2)^{ - 1}}]$ and $ m$ is a multiplier for the $ {\operatorname{Ad} _G}$-invariant $ {L^p}$ functions on $ \mathfrak{g}$, then the restriction of a translate of $ m$ to $ \hat G$ is a multiplier for the central $ {L^p}$ functions on $ G$.

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Keywords: $ {L^p}$ multiplier, invariant function
Article copyright: © Copyright 1976 American Mathematical Society