Interpolation of Morrey-Campanato and Related Smoothness Spaces

TL;DR

This paper investigates the interpolation properties of Morrey-Campanato and related smoothness spaces using various methods, with a focus on quasi-Banach spaces and the interpolation property.

Contribution

It provides new insights into the interpolation of Morrey-Campanato and related spaces, including Besov-type and Triebel-Lizorkin-type spaces, using multiple interpolation techniques.

Findings

Analysis of the complex, ±-, and Peetre-Gagliardo interpolation methods.

Results on the interpolation property in quasi-Banach spaces.

Extensions to Besov-type and Triebel-Lizorkin-type spaces.

Abstract

In this article, the authors study the interpolation of Morrey-Campanato spaces and some smoothness spaces based on Morrey spaces, e.\,g., Besov-type and Triebel-Lizorkin-type spaces. Various interpolation methods, including the complex method, the $\pm$-method and the Peetre-Gagliardo method, are studied in such a framework. Special emphasize is given to the quasi-Banach case and to the interpolation property.