IUMJ

Title: Hardy inequalities in Triebel--Lizorkin spaces

Authors: Lizaveta Ihnatsyeva and Antti Vahakangas

Issue: Volume 62 (2013), Issue 6, 1785-1807

Abstract:

We prove an inequality of Hardy type for functions in Triebel-Lizorkin spaces. The distance involved is measured to a given Ahlfors $d$-regular set in $\mathbb{R}^n$, with $n-1<d<n$. As an application of the Hardy inequality, we consider boundedness of pointwise multiplication operators, and extension problems.