Trace Hardy--Sobolev--Mazy'a inequalities for the half fractional   Laplacian
  In this work we establish trace Hardy-Sobolev-Maz'ya inequalities with best Hardy constants, for weakly mean convex domains. We accomplish this by obtaining a new weighted Hardy type estimate which is of independent inerest. We then produce Hardy-Sobolev-Maz'ya inequalities for the spectral half Laplacian. This covers a critical case left open in \cite{FMT1}. 
Stathis Filippas, Luisa Moschini and Achilles Tertikas
math.AP math.SP