Reduction principle for Gaussian $K$-inequality

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.

20 pages

References in corpus (2)

• On the properties of quasi-Banach function spaces
• Lorentz--Karamata spaces

Cited by in corpus (4)

• On the smoothness of slowly varying functions
• On the properties of rearrangement-invariant quasi-Banach function spaces
• Non-improvability of sharp endpoint estimates
• Potential trace inequalities via a Calderón-type theorem