论文标题
径向对称性的分数超级和亚谐波函数的紧凑型嵌入
Compact embeddings for fractional super and sub harmonic functions with radial symmetry
论文作者
论文摘要
我们证明了嵌入在Sobolev空间中的紧凑性，用于具有径向对称性的分数超级和亚谐波函数。主要工具是属于有限同质Sobolev Norm定义的函数空间的径向对称函数的重点衰减，以及Riesz电位的有限$ l^2 $ NORM。作为副产品，我们也证明了sobolev空间中插值不平等的最大化剂，用于径向对称的分数超级和亚谐波函数。
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.
