This book is intended as a survey of latest results on weighted inequalities in Lorentz, Orlicz spaces and Zygmund classes. During the last few years they have become one of the mostdeveloped offshoots of the theory of the harmonic analysis operators. Up to now there has been no monograph devoted to these questions, the results are mostly scattered in various journals and a part of the book consists of results not published anywhere else. Many of theorems presented have only previously been published in Russian.
Integral operators in nonweighted Orlicz classes; maximal functions and potentials in weighted Orlicz classes; singular integrals in weighted Orlicz classes; integral operators in weighted Zygmund classes; fractional maximal function in weighted Lorentz spaces; potentials and Riesz transforms in weighted Lorentz spaces.