Variable exponent Sobolev spaces associated with Jacobi expansions

TL;DR

This paper introduces variable exponent Sobolev spaces linked to Jacobi expansions and characterizes them as potential and Triebel-Lizorkin type spaces, expanding the functional analysis framework in this context.

Contribution

The paper defines and characterizes variable exponent Sobolev spaces associated with Jacobi expansions, connecting them to potential and Triebel-Lizorkin spaces for the first time.

Findings

Sobolev spaces characterized as potential spaces

Sobolev spaces characterized as Triebel-Lizorkin spaces

Extension of functional analysis in Jacobi expansion context

Abstract

In this paper we define variable exponent Sobolev spaces associated with Jacobi expansions. We prove that our generalized Sobolev spaces can be characterized as variable exponent potential spaces and as variable exponent Triebel-Lizorkin type spaces.