Spectral Integration of Marcinkiewicz Multipliers

Nakhlé H. Asmar, Earl Berkson, T. A. Gillespie

Type: Article

Publication Date: 1993-06-01

Citations: 3

DOI: https://doi.org/10.4153/cjm-1993-024-7

Abstract

Abstract Let X be a closed subspace of L P ( 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.

Locations

Canadian Journal of Mathematics - View - PDF

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Works Cited by This (5)

Action	Title	Year	Authors
+	Representations of groups with ordered duals and generalized analyticity	1990	Nakhlé H. Asmar Earl Berkson T. A. Gillespie
+	On the almost everywhere convergence of ergodic averages for power-bounded operators on LP-subspaces	1991	Earl Berkson Jean Bourgain T. A. Gillespie
+	Abstract Spectral Decompositions Guaranteed by the Hilbert Transform	1986	Earl Berkson T. A. Gillespie Paul S. Muhly
+	Spectral Theory for Linear Operators	2018	Pierre Magal Shigui Ruan
+	Classical Banach Spaces I	1977	Joram Lindenstrauss Lior Tzafriri