Optimal domain and integral extension of operators: acting in function spaces

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. Many and varied examples to supplement thetheory. Interdisciplinary character. Most material appears in print for the first time. Extensive bibliography INDICE: 1. Introduction.- 2. Quasi-Banach Function Spaces.- 3. Vector Measures and Integration Operators.- 4. Optimal Domains and Integral Extensions.- 5. Operators which are p-th Power Factorable.- 6. Factorization of p-th Power Factorable Operators through Lp-Spaces.- 7. Operators from Classical Harmonic Analysis.

• ISBN: 978-3-7643-8647-4
• Editorial: Birkhaüser
• Encuadernacion: Cartoné
• Páginas: 400
• Fecha Publicación: 01/05/2008
• Nº Volúmenes: 1
• Idioma: Inglés