We prove a “multiplier” result for functions of the infinitesimal generator 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 ℒ in the case when the Lp-operator norm of ℒm has polynomial growth at infinity. In particular, we prove a “multiplier” result of Marcinkiewicz type for functions of 3*
Meda, S. (1990). A general multiplier theorem. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 110(3), 639-647 [10.1090/S0002-9939-1990-1028046-7].
A general multiplier theorem
MEDA, STEFANO
1990
Abstract
We prove a “multiplier” result for functions of the infinitesimal generator 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 ℒ in the case when the Lp-operator norm of ℒm has polynomial growth at infinity. In particular, we prove a “multiplier” result of Marcinkiewicz type for functions of 3*
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