论文标题
在2D球体上的一类插值不平等现象上
On a class of interpolation inequalities on the 2D sphere
论文作者
论文摘要
我们证明了$ l^p $ - 函数系统和差异的矢量函数的$ l^p $ norms，这些功能在sobolev space $ h^1 $在2D球体上是正直的。作为推论，在gagliardo-nirenberg interpolation不平等中获得了嵌入$ h^1 \ hookrightarrow l^q $，$ q <\ infty $的订单尖锐常数。
We prove estimates for the $L^p$-norms of systems of functions and divergence free vector functions that are orthonormal in the Sobolev space $H^1$ on the 2D sphere. As a corollary, order sharp constants in the embedding $H^1\hookrightarrow L^q$, $q<\infty$, are obtained in the Gagliardo--Nirenberg interpolation inequalities.
