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arXiv · 2201.09238

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

Jacopo Bellazzini·Vladimir Georgiev
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Abstract

We prove compactness of the embeddings in Sobolev spaces for fractional super and sub harmonic functions with radial symmetry. The main tool is a pointwise decay for radially symmetric functions belonging to a function space defined by finite homogeneous Sobolev norm together with finite $L^2$ norm of the Riesz potentials. As a byproduct we prove also existence of maximizers for the interpolation inequalities in Sobolev spaces for radially symmetric fractional super and sub harmonic functions.

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Jacopo Bellazzini, Vladimir Georgiev. 2022-01-23. Compact embeddings for fractional super and sub harmonic functions with radial symmetry. https://arxiv.org/abs/2201.09238

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