Optimal Domain and Integral Extension of Operators

"This book treats the analysis of linear operators from a quasi-Banach function space into a Banach space. The idea is to extend the operator to its optimal domain space and to take advantage of this in analysing the original operator. Of particular interest are ideal properties such as compactness, weak compactness and complete continuity." "Since the book is directed not only at experienced researchers but also advanced research students, complete proofs are included and examples are worked out in detail. A good working knowledge of functional analysis, measure theory, operator theory and commutative harmonic analysis is assumed, whereas any new material is developed in a self-contained manners."--BOOK JACKET.