Orlicz-Lorentz Gauge functional inequalities for some integral operators

Abstract

Let $f\in M_{+}({\mathbb{R}}_{+})$, the class of nonnegative, Lebesgure-measurable functions on ${\mathbb{R}}_{+}=(0,\infty )$. We deal with integral operators of the form \[ (T_Kf)(x)=\int_{\mathbb{R}_+}K(x,y)f(y)\, dy, \quad x \in \mathbb{R}_+, \] with $K\in M_{+}({\mathbb{R}}_{+}^2)$.