The present monograph serves as a natural extension of the prior 2-volume monograph with the same title and by the same authors, which encompassed findings up until 2014. This four-volume project encapsulates the authors' decade-long research in the trending topic of nonstandard function spaces and operator theory.

One of the main novelties of the present book is to develop the extrapolation theory, generally speaking, in grand Banach function spaces, and to apply it for obtaining the boundedness of fundamental operators of harmonic analysis, in particular, function spaces such as grand weighted Lebesgue and Lorentz spaces, grand variable exponent Lebesgue/Morrey spaces, mixed normed function spaces, etc. Embeddings in grand variable exponent Hajasz-Sobolev spaces are also studied. Some applications to the approximation theory and boundary value problems of analytic functions are presented as well.

The book is aimed at an audience ranging from researchers in operator theory and harmonic analysis to experts in applied mathematics and post graduate students. In particular, we hope that this book will serve as a source of inspiration for researchers in abstract harmonic analysis, function spaces, PDEs and boundary value problems.

Provides a comprehensive overview of the past decade's developments in the realm of non-standard function spaces Covers an extensive range of results in the theory of integral operators, encompassing the linear and multilinear cases Written for a broad audience, ranging from researchers to experts in applied mathematics and prospective students

Inhalt

• 18. Integral Operators on Weighted Grand Lebesgue Spaces (WGLS) .- 19. Integral Operators in Grand Mixed-Normed Function Spaces.- 20. Grand Variable Exponent Function Spaces.- 21. Extrapolation in Grand Function Spaces.- 22. Grand Variable Haj laszSobolev and Hölder Spaces.- 23. Grand Lebesgue Type Spaces.