Criteria for boundedness of a class of integral operators from $L_p$ to $L_q$ for $1<q<p<\infty$

TL;DR

This paper establishes new criteria for the boundedness of a class of integral operators with non-negative kernels from $L_p$ to $L_q$ spaces, relaxing previous conditions and broadening applicability.

Contribution

It introduces less restrictive conditions on kernels for boundedness criteria of integral operators between Lebesgue spaces.

Findings

Derived new boundedness criteria for integral operators

Extended applicability to broader kernel classes

Provided theoretical conditions for operator boundedness

Abstract

In the paper, we consider integral operators with non-negative kernels satisfying conditions, which are less restrictive than conditions studied earlier. We establish criteria for the boundedness of these operators in Lebesgue spaces.