Integral Operators in Non-Standard Function Spaces, Softcover reprint of the original 1st ed. 2016 Volume 1: Variable Exponent Lebesgue and Amalgam Spaces Operator Theory: Advances and Applications Series, Vol. 248

This book, the result of the authors' long and fruitful collaboration, focuses on integral operators in new, non-standard function spaces and presents a systematic study of the boundedness and compactness properties of basic, harmonic analysis integral operators in the following function spaces, among others: variable exponent Lebesgue and amalgam spaces, variable Hölder spaces, variable exponent Campanato, Morrey and Herz spaces, Iwaniec-Sbordone (grand Lebesgue) spaces, grand variable exponent Lebesgue spaces unifying the two spaces mentioned above, grand Morrey spaces, generalized grand Morrey spaces, and weighted analogues of some of them.

The results obtained are widely applied to non-linear PDEs, singular integrals and PDO theory. One of the book's most distinctive features is that the majority of the statements proved here are in the form of criteria.

The book is intended for a broad audience, ranging from researchers in the area to experts in applied mathematics and prospective students.

Presents the first comprehensive account of the two-weight theory of basic integral operators, developed in variable exponent Lebesgue spaces

Provides the complete characterizations of Riesz potentials (of functions in variable Lebesgue spaces), weights and space exponents

Explores the weak and strong type estimates criteria for fractional and singular integrals

Introduces new function spaces that unify variable exponent Lebesgue spaces and grand Lebesgue spaces