Interpolation with a function parameter and refined scale of spaces

TL;DR

This paper explores the interpolation of Hilbert space pairs using a function parameter, establishing fundamental properties and applying these results to isotropic Hörmander spaces on closed manifolds.

Contribution

It introduces a refined interpolation method with a function parameter and demonstrates its application to Hörmander spaces, extending classical interpolation theory.

Findings

Established main properties of the function-parameter interpolation

Applied interpolation results to isotropic Hörmander spaces

Extended classical interpolation theory to new function spaces

Abstract

The interpolation of couples of separable Hilbert spaces with a function parameter is studied. The main properties of the classic interpolation are proved. Some applications to the interpolation of isotropic H\"ormander spaces over a closed manifold are given.