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We prove compactness of the embeddings in Sobolev spaces for fractional superand sub harmonic functions with radial symmetry. The main tool is a pointwisedecay for radially symmetric functions belonging to a function space defined byfinite homogeneous Sobolev norm together with finite $L^2$ norm of the Rieszpotentials. As a byproduct we prove also existence of maximizers for theinterpolation inequalities in Sobolev spaces for radially symmetric fractionalsuper and sub harmonic functions.

Compact embeddings for fractional super and sub harmonic functions with radial symmetry