论文标题
在伯恩斯坦和marcinkiewicz型不平等上，多变量$ c^α$ domains
On Bernstein- and Marcinkiewicz-type inequalities on multivariate $C^α$-domains
论文作者
论文摘要
我们证明了与普通紧凑型$ c^α$ domain在$ 1 \leqα\ leq 2 $的一般紧凑型$ c^α$ domain边界上的$ l^p $空间中的新伯恩斯坦和马尔可夫类型的不等式。这些估计还适用于建立Marcinkiewicz型不平等，以在$ c^α$ domains上离散$ l^p $ norms of代数多项式，并具有渐近最佳的函数样本。
We prove new Bernstein and Markov type inequalities in $L^p$ spaces associated with the normal and the tangential derivatives on the boundary of a general compact $C^α$-domain with $1\leq α\leq 2$. These estimates are also applied to establish Marcinkiewicz type inequalities for discretization of $L^p$ norms of algebraic polynomials on $C^α$-domains with asymptotically optimal number of function samples used.
