# Higher order derivatives of analytic families of Banach spaces

## TL;DR

This paper investigates the structure of Rochberg spaces generated by complex interpolation of analytic Banach space families, establishing their interpolation properties and deriving associated spaces and derivations.

## Contribution

It demonstrates that Rochberg spaces from complex interpolation form their own interpolation scales and characterizes the resulting spaces and derivations.

## Key findings

- Rochberg spaces form complex interpolation scales
- Explicit description of interpolated spaces and derivations
- Application to analytic families of Banach spaces

## Abstract

We show that the Rochberg spaces induced by complex interpolation form themselves complex interpolation scales, obtain the interpolated spaces and associated derivations. We present our results in the context of analytic families of Banach spaces and study the problem of determining the Rochberg spaces induced by these new families.