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Trace Hardy--Sobolev--Maz'ya inequalities for the half fractional Laplacian

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  • 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 [9].
    Mathematics Subject Classification: Primary: 35J60, 42B20, 46E35; Secondary: 26D10, 35J15, 35P15, 47G30.

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