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Spectral Integration of Marcinkiewicz Multipliers

Published online by Cambridge University Press:  20 November 2018

Nakhlé Asmar ,
Earl Berkson  and
T. A. Gillespie
Nakhlé Asmar
Affiliation:
Department of Mathematics, University of Missouri-Columbia, Columbia, Missouri 65211, U.S.A
Earl Berkson
Affiliation:
University of Illinois, Department of Mathematics, 1409 West Green Street, Urbana, Illinois 61801, U.S.A.
T. A. Gillespie
Affiliation:
Department of Mathematics, University of Edinburgh, James Clerk Maxwell Building, Edinburgh EH9 3JZ, Scotland
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Abstract

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Let X be a closed subspace of LP(μ), where μ is an arbitrary measure and 1 < p < ∞. By extending the scope of spectral integration, we show that every invertible power-bounded linear mapping of X into X has a functional calculus implemented by the algebra of complex-valued functions on the unit circle satisfying the hypotheses of the Strong Marcinkiewicz Multiplier Theorem. This result expands the framework of the Strong Marcinkiewicz Multiplier Theorem to the setting of abstract measure spaces.

Keywords

42A4547B40
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 45 , Issue 3 , 01 June 1993 , pp. 470 - 482
Copyright
Copyright © Canadian Mathematical Society 1993

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