Optimal Hardy inequality for the fractional Laplacian on $L^p$

TL;DR

This paper establishes the optimal Hardy inequality for the fractional Laplacian in L^p spaces and characterizes the contractivity of related Feynman-Kac semigroups, advancing understanding of fractional operators.

Contribution

It provides the first explicit L^p Hardy inequality for the fractional Laplacian and characterizes semigroup contractivity in this setting.

Findings

Optimal Hardy inequality in L^p for fractional Laplacian

Explicit characterization of Feynman-Kac semigroup contractivity

Advancement in fractional operator analysis

Abstract

For the fractional Laplacian we give Hardy inequality which is optimal in $L^p$ for $1<p<\infty$. As an application, we explicitly characterize the contractivity of the corresponding Feynman-Kac semigroups on $L^p$.