This volume, as a sequel to Volumes I-IV of "Integral Operators in Non-Standard Function Spaces", is devoted to the authors’ most recent advances in harmonic analysis and their applications.

This volume focusses on Rellich inequalities in the variable exponent and multilinear settings, trace inequalities for linear and multilinear fractional integrals, sharp weighted estimates for norms of operators of harmonic analysis, criteria governing Sobolev-type inequalities for (generalized) fractional integrals associated with non-doubling measures, sharp Olsen-type inequalities, studies on Herz-type spaces, approximation in subspaces of Morrey spaces, introduction of variable exponent bounded variation spaces in the Riesz sense, and characterization of weighted Sobolev spaces via weighted Riesz bounded variation spaces.

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, it is hoped that this book will serve as a source of inspiration for researchers in abstract harmonic analysis, function spaces, PDEs and boundary value problems.