Integral Operators in Non-Standard Function Spaces: Volume 3: Advances in Grand Function Spaces

Kokilashvili, Vakhtang; Meskhi, Alexander; Rafeiro, Humberto; Samko, Stefan

ISBN 10: 3031649826 / ISBN 13: 9783031649820

Published by Birkhäuser, 2024

About this Item

Seller Inventory # 26401183810

Bibliographic Details

Title: Integral Operators in Non-Standard Function ...

Publisher: Birkhäuser

Publication Date: 2024

Binding: Hardcover

Condition: New

About this title

Synopsis:

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 Hajłasz-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.