Logarithmic interpolation methods, measure of non-compactness of bilinear operators and function spaces of Lorentz-Sobolev type

Abstract

The guiding theme and main topic of this monograph is Interpolation Theory. However, as it is suggested by the title, we can distinguish three different parts: the first one covers Chapters 3‐7 and it focuses on the study of the so‐called logarithmic interpolation methods. As for the second one, it consists of Chapter 8 and concentrates on the research of some properties related to the interpolation of bilinear operators, this time by the real method and some of its variants. Finally, the third part, containing Chapters 9 and 10, examines function spaces of Lorentz‐Sobolev type, in particular, Besov‐Lorentz and Triebel‐Lizorkin‐Lorentz spaces and it studies some of its properties by means of different interpolation results.Interpolation Theory is a branch of Functional Analysis with important applications to Partial Differential Equations, Harmonic Analysis, Approximation Theory, Function Spaces and Operators Theory, among other areas in mathematics. Reference sources for the subject are, for example, the books by Bennett and Sharpley [6], Bergh and Löfström [11], Butzer and Berens [23], Brudnyĭ and Krugljak [22], König [84] and Triebel [110]...