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A general multiplier theorem


Author: Stefano Meda
Journal: Proc. Amer. Math. Soc. 110 (1990), 639-647
MSC: Primary 42A45; Secondary 47D03
DOI: https://doi.org/10.1090/S0002-9939-1990-1028046-7
MathSciNet review: 1028046
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Abstract: We prove a "multiplier" result for functions of the infinitesimal generator $ \mathcal{L}$ of a symmetric semigroup, which generalizes some previous results by E. M. Stein and M. G. Cowling. As an application, we develop a functional calculus for $ \mathcal{L}$ in the case when the $ {L^p}$-operator norm of $ {\mathcal{L}^{iu}}$ has polynomial growth at infinity. In particular, we prove a "multiplier" result of Marcinkiewicz type for functions of $ \mathcal{L}$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1990-1028046-7
Keywords: Multiplier operator, Mellin transform, $ g$-function
Article copyright: © Copyright 1990 American Mathematical Society

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