A note on the fractional Hardy inequality
Matteo Aldovardi, Jacopo Bellazzini
TL;DR
This paper provides a direct proof of the fractional Hardy inequality using Littlewood-Paley decomposition and properties of singular kernels, including a refinement for cases where q>2.
Contribution
It introduces a new direct proof method for the fractional Hardy inequality and offers a refinement for the case q>2.
Findings
Direct proof of fractional Hardy inequality established
Refinement of the inequality for q>2
Utilizes Littlewood-Paley decomposition and singular kernel properties
Abstract
We give a direct proof of fractional Hardy inequality by means of Littlewood-Paley decomposition and properties of singular homogeneous kernels of degree -. A refinement when is proved.
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Nonlinear Partial Differential Equations · Differential Equations and Boundary Problems