Optimal Domain and Integral Extension of Operators [electronic resource] :Acting in Function Spaces / by Susumu Okada, Werner J. Ricker, Enrique A. Sánchez Pérez.
by Okada, Susumu [author.]; Ricker, Werner J [author.]; Sánchez Pérez, Enrique A [author.]; SpringerLink (Online service).
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Quasi-Banach Function Spaces -- Vector Measures and Integration Operators -- Optimal Domains and Integral Extensions -- p-th Power Factorable Operators -- Factorization of p-th Power Factorable Operators through Lq-spaces -- Operators from Classical Harmonic Analysis.
This book deals with the analysis of linear operators from a quasi-Banach function space into a Banach space. The central theme is to extend the operator to as large a (function) space as possible, its optimal domain, and to take advantage of this in analyzing the original operator. Applications are given to Maurey-Rosenthal factorization of operators and to classical operators arising in commutative harmonic analysis. The main tool is the vector measure associated to such an operator, which produces a corresponding space of integrable functions and an integration operator.
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