论文标题
$ l^p $ -Bernstein的不平等现象，$ C^2 $ - 域名和申请
$L^p$-Bernstein inequalities on $C^2$-domains and applications to discretization
论文作者
论文摘要
我们证明了与一般紧凑型$ c^2 $ domain边界上的切向衍生品相关的$ l^p $空间中的新伯恩斯坦类型不平等。我们提供了两个应用程序：Marcinkiewicz类型的不平等，用于离散$ l^p $ norm和正数立方体公式。从某种意义上说，这两个结果都是最佳的，因为所使用的函数样本的数量具有代数多项式相应空间的维度的顺序。
We prove a new Bernstein type inequality in $L^p$ spaces associated with the tangential derivatives on the boundary of a general compact $C^2$-domain. We give two applications: Marcinkiewicz type inequality for discretization of $L^p$ norm and positive cubature formula. Both results are optimal in the sense that the number of function samples used has the order of the dimension of the corresponding space of algebraic polynomials.
