Hardy inequalities in Triebel-Lizorkin spaces II. Aikawa dimension

TL;DR

This paper establishes Hardy inequalities for functions in Triebel-Lizorkin spaces on domains with boundaries having Aikawa dimension less than a critical threshold, extending the understanding of boundary behavior in these function spaces.

Contribution

It proves Hardy inequalities in Triebel-Lizorkin spaces for domains with boundaries of Aikawa dimension below a specific limit, advancing boundary regularity analysis.

Findings

Hardy inequalities hold for domains with boundary Aikawa dimension < n - sp

Extension of Hardy inequalities to Triebel-Lizorkin spaces

Boundary regularity characterized by Aikawa dimension

Abstract

We prove inequalities of Hardy type for functions in Triebel-Lizorkin spaces $F^s_{pq}(G)$ on a domain $G\subset\mathbb{R}^n$, whose boundary has the Aikawa dimension strictly less than $n-sp$.