A Functorial Approach to Multi-Space Interpolation with Function Parameters

TL;DR

This paper develops a functorial framework for multi-space interpolation using functional parameters, enabling the construction of generalized intermediate spaces and applications to Sobolev and Besov spaces.

Contribution

It extends interpolation theory to multiple spaces with a systematic functorial approach, including explicit tools and stability properties.

Findings

Interpolation of multiple Sobolev spaces yields generalized Besov spaces

Framework ensures stability under powers and convex combinations

Provides explicit tools for multi-parameter interpolation

Abstract

We introduce an extension of interpolation theory to more than two spaces by employing a functional parameter, while retaining a fully functorial and systematic framework. This approach allows for the construction of generalized intermediate spaces and ensures stability under natural operations such as powers and convex combinations. As a significant application, we demonstrate that the interpolation of multiple generalized Sobolev spaces yields a generalized Besov space. Our framework provides explicit tools for handling multi-parameter interpolation, highlighting both its theoretical robustness and practical relevance.