Hardy inequalities in Triebel--Lizorkin spaces
Lizaveta IhnatsyevaAntti Vähäkangas
46E35Ahlfors d-regular setHardy inequalitypointwise multiplierextension theoremlocal polynomial approximation
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.
Indiana University Mathematics Journal
2013
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10.1512/iumj.2013.62.5173
10.1512/iumj.2013.62.5173
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Indiana Univ. Math. J. 62 (2013) 1785 - 1807
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