Reduction principle for Gaussian $K$-inequality

TL;DR

This paper investigates the interpolation properties of certain nonlinear operators satisfying a specific K-inequality related to Gaussian--Sobolev embeddings, establishing a reduction principle for a broad class of these operators.

Contribution

It introduces a reduction principle for operators satisfying a K-inequality in the context of Gaussian--Sobolev embeddings, expanding understanding of their interpolation properties.

Findings

Established a reduction principle for a wide class of operators

Characterized interpolation properties related to Gaussian--Sobolev embeddings

Extended the theory of K-inequalities in functional analysis

Abstract

We study interpolation properties of operators (not necessarily linear) which satisfy a specific $K$-inequality corresponding to endpoints defined in terms of Orlicz--Karamata spaces modeled upon the example of the Gaussian--Sobolev embedding. We prove a reduction principle for a fairly wide class of such operators.