The monograph presents some of the authors' recent and original results concerning boundedness and compactness problems in Banach function spaces both for classical operators and integral transforms defined, generally speaking, on nonhomogeneous spaces. Itfocuses onintegral operators naturally arising in boundary value problems for PDE, the spectral theory of differential operators, continuum and quantum mechanics, stochastic processes etc. The book may be considered as a systematic and detailed analysis of a large class of specific integral operators from the boundedness and compactness...

An analysis of a wide class of integral transforms with product kernels from the two-weighted boundedness point of view. This book discusses weighted integral in-equalities for monotonic functions of several variables.

Deals with the measure of non-compactness (essential norm) in weighted Lebesgue spaces for maximal, potential and singular operators dened, generally speaking, on homogeneous groups. This book presents an analysis of a class of specific integral operators from the boundedness/compactness or non-compactness point of view.

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...