Integral operators on grand Lebesgue spaces and related weights with properties

Abstract

A number of properties for the classes $B_p^{-1}$ and $B_p^{*}$ have been proved. The class $B_p^{-1}$ characterizes the $L^p$- inequality involving the averaging operator and the class $B_p^{*}$ characterizes the $L^p$- inequality involving the adjoint averaging operator. The reverse inequalities involving the integral operators in $L^{p)}_w$ have also been studied.