Stein interpolation for the real interpolation method

TL;DR

This paper introduces a complex formulation of the real interpolation method, enabling Stein interpolation for it, and applies this to weighted spaces and operator sectoriality.

Contribution

It provides the first complex formulation of the real interpolation method and proves Stein interpolation within this framework.

Findings

Established a complex formulation of the real interpolation method.

Proved Stein interpolation for the real interpolation method.

Applied the theorem to weighted L^p spaces and operator sectoriality.

Abstract

We prove a complex formulation of the real interpolation method, showing that the real and complex interpolation methods are not inherently real or complex. Using this complex formulation, we prove Stein interpolation for the real interpolation method. We apply this theorem to interpolate weighted $L^p$-spaces and the sectoriality of closed operators with the real interpolation method.