Extrapolation of operator-valued multiplication operators

TL;DR

This paper explores the extrapolation of operator-valued multiplication operators within L^p fiber spaces, motivated by applications in non-autonomous evolution equations, providing insights into their structure and behavior.

Contribution

It introduces a framework for extrapolating unbounded multiplication operators in L^p fiber spaces, advancing understanding of their properties in non-autonomous evolution contexts.

Findings

Characterization of L^p fiber spaces related to multiplication operators

Analysis of extrapolation techniques for unbounded operators

Applications to non-autonomous evolution equations

Abstract

We discuss $\mathrm{L}^p$ fiber spaces which appear, e.g., as extrapolation spaces of unbounded multiplication operators which in turn are motivated, for instance, by non-autonomous evolution equations.