Interpolation of uniformly absolutely continuous operators

Abstract

We develop a method suitable for interpolation of uniformly absolutely continuous operators. We then apply this method to establishing compactness of operators and embeddings especially in the limiting situations, where the classical interpolation methods fail.

We study types of certain interpolation methods and their sharpness.

Keywords

• Uniformly absolutely continuous operators
• interpolation
• compactness
• quasiconcave function
• weighted inequalities
• K-functional