Some remarks on the interpolation space A^\beta

TL;DR

This paper demonstrates that the complex interpolation space remains consistent regardless of the method used to define it, clarifying a fundamental aspect of interpolation theory.

Contribution

It establishes the equivalence of two different methods for constructing the complex interpolation space, providing a clearer understanding of its properties.

Findings

Confirmed the equivalence of the two interpolation methods

Simplified the conceptual understanding of complex interpolation spaces

Contributed to the theoretical foundation of interpolation theory

Abstract

In this work, we show that the complex interpolation space is the same by the two methods.