Weighted inequalities for quasilinear integral operators on the semiaxis and application to the Lorentz spaces

TL;DR

This paper characterizes weighted inequalities for positive quasilinear integral operators with Oinarov's kernel on the semiaxis and applies these results to the boundedness of maximal operators in Lorentz spaces.

Contribution

It provides a comprehensive characterization of weighted inequalities for a class of integral operators and applies these to Lorentz space boundedness.

Findings

Weighted inequalities are established for quasilinear integral operators.

Boundedness of maximal operators in Lorentz spaces is demonstrated.

Results extend existing inequalities to more general weights and kernels.

Abstract

Weighted $L^p-L^r$ inequalities with arbitrary measurable non-negative weights for positive quasilinear integral operators with Oinarov's kernel on the semiaxis are characterized. Application to the boundedness of maximal operator in the Lorentz $\Gamma-$spaces is given.