Fractional Hardy-Sobolev-Maz'ya inequality on balls and halfspaces

We prove fractional Hardy–Sobolev–Maz’ya inequality for balls and a half-space, partially answering the open problem posed by Frank and Seiringer [arXiv:0906.1561v1 [math.FA], 2009] We note that for half-spaces this inequality has been recently obtained by Sloane [arXiv:1004.4828v1 [math.FA], 2010].