Orlicz-Lorentz Gauge functional inequalities for some integral operators

TL;DR

This paper investigates gauge functional inequalities within Orlicz-Lorentz spaces for certain integral operators, providing new bounds and conditions for their boundedness.

Contribution

It introduces novel gauge functional inequalities for integral operators in Orlicz-Lorentz spaces, expanding the understanding of their boundedness and behavior.

Findings

Established new inequalities for integral operators in Orlicz-Lorentz spaces

Derived conditions for the boundedness of these operators

Extended classical results to a broader functional framework

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 $K \in M_+(\mathbb{R}_+^2)$.