On potential spaces related to Jacobi expansions

TL;DR

This paper explores potential spaces linked to Jacobi expansions, establishing their structure, embeddings, and characterizations, and demonstrating applications to PDEs.

Contribution

It introduces new structural and Sobolev embedding theorems for Jacobi potential spaces and characterizes them via fractional square functions.

Findings

Established Sobolev-type embedding theorems

Characterized Jacobi potential spaces with fractional square functions

Applied results to PDE problems

Abstract

We investigate potential spaces associated with Jacobi expansions. We prove structural and Sobolev-type embedding theorems for these spaces. We also establish their characterizations in terms of suitably defined fractional square functions. Finally, we present sample applications of the Jacobi potential spaces connected with a PDE problem.