Geodesic
Best Constant in the Weighted Hardy Inequality: The Spatial and Spherical Version
Fractional calculus and applied analysis, Tome 8 (2005) no. 1, pp. 39-52

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The sharp constant is obtained for the Hardy-Stein-Weiss inequality for fractional Riesz potential operator in the space L^p(R^n, ρ) with the power weight ρ = |x|^β. As a corollary, the sharp constant is found for a similar weighted inequality for fractional powers of the Beltrami-Laplace operator on the unit sphere.
Keywords: Hardy Inequality, Rellich Inequality, Fractional Powers, Riesz Potentials, Beltrami-Laplace Operator, Stereographic Projection, 26D10 
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Samko, Stefan. Best Constant in the Weighted Hardy Inequality: The Spatial and Spherical Version. Fractional calculus and applied analysis, Tome 8 (2005) no. 1, pp. 39-52. http://geodesic.mathdoc.fr/item/FCAA_2005_8_1_a1/