Complex interpolation of Orlicz sequence spaces and its higher order Rochberg spaces

TL;DR

This paper investigates the complex interpolation of Orlicz sequence spaces, demonstrating that the associated Rochberg derived spaces are Fenchel-Orlicz spaces and exploring their extension properties.

Contribution

It establishes the structure of higher order Rochberg spaces for Orlicz sequence spaces as Fenchel-Orlicz spaces, revealing new properties of their twisted sums.

Findings

Rochberg derived spaces are Fenchel-Orlicz spaces

Twisted sums have the (C[0,1], C)-extension property

Results apply to suitable Orlicz sequence space couples

Abstract

We show that if $(\ell_{\phi_0}, \ell_{\phi_1})$ is a couple of suitable Orlicz sequence spaces then the corresponding Rochberg derived spaces of all orders associated to the complex interpolation method are Fenchel-Orlicz spaces. In particular, the induced twisted sums have the $(C[0, 1], \mathbb{C})$-extension property.