简介
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.
目录
Contents 6
Preface 8
Chapter 1 Introduction 12
Chapter 2 Quasi-Banach Function Spaces 28
Chapter 3 Vector Measures and Integration Operators 113
Chapter 4 Optimal Domains and Integral Extensions 190
Chapter 5 p-th Power Factorable Operators 217
Chapter 6 Factorization of p-th Power Factorable Operators through Lq-spaces 244
Chapter 7 Operators from Classical Harmonic Analysis 301
Bibliography 385
List of Symbols 395
Index 400
Preface 8
Chapter 1 Introduction 12
Chapter 2 Quasi-Banach Function Spaces 28
Chapter 3 Vector Measures and Integration Operators 113
Chapter 4 Optimal Domains and Integral Extensions 190
Chapter 5 p-th Power Factorable Operators 217
Chapter 6 Factorization of p-th Power Factorable Operators through Lq-spaces 244
Chapter 7 Operators from Classical Harmonic Analysis 301
Bibliography 385
List of Symbols 395
Index 400
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