Complex interpolation of variable Triebel-Lizorkin spaces

TL;DR

This paper investigates the complex interpolation properties of variable Triebel-Lizorkin spaces, providing new interpolation results and exploring limiting cases to deepen understanding of these function spaces.

Contribution

It introduces new complex interpolation results for variable Triebel-Lizorkin spaces and examines their limiting cases, advancing the theoretical framework of these spaces.

Findings

Derived complex interpolation formulas for $F_{p(ullet),q}^{ullet}$ spaces.

Established interpolation results for $F_{p(ullet),p(ullet)}^{ullet(ullet)}$ spaces.

Analyzed limiting cases of the interpolation process.

Abstract

We study complex interpolation of variable Triebel-Lizorkin spaces, especially we present the complex interpolation of $F_{p(\cdot),q}^{\alpha }$ and $F_{p(\cdot ),p(\cdot )}^{\alpha (\cdot )}$ spaces. Also, some limiting cases are given.