The fractional Hardy inequality with a remainder term

Abstract

We calculate the regional fractional Laplacian on some power function on an interval. As an application, we prove Hardy inequality with an extra term for the fractional Laplacian on the interval with the optimal constant. As a result, we obtain the fractional Hardy inequality with best constant and an extra lower-order term for general domains, following the method developed by M. Loss and C. Sloane [arXiv:0907.3054v1 [math.AP]]

Major changes

Cited by in corpus (11)

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• Nonlocally-induced (fractional) bound states: Shape analysis in the infinite Cauchy well
• Some Ostrowski type inequalities via Riemann-Liouville fractional integrals for h-convex functions
• Fractional Hardy-Sobolev-Maz'ya inequality for domains
• Ultrarelativistic (Cauchy) spectral problem in the infinite well
• Fractional Hardy-Sobolev-Maz'ya inequality on balls and halfspaces
• The Poisson problem for the fractional Hardy operator: Distributional identities and singular solutions