A general multiplier theorem

Meda, Stefano

doi:10.1090/S0002-9939-1990-1028046-7

A general multiplier theorem
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by Stefano Meda PDF

Proc. Amer. Math. Soc. 110 (1990), 639-647 Request permission

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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Topics in harmonic analysis related to the Littlewood-Paley theory

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