L^(2)空间中的Bernstein-Markov不等式

Bernstein-Markov type inequalities in L^(2) space

文章证明了对于次数不超过 n的代数多项式 f(x)有∫1- 1|f′(x) |2 dx≤ 12 4 (n+1 ) (2 n+1 ) (2 n2 +7n +3) ∫1- 1|f(x) |2 dx,右端的最佳常数在 11 0 n4 +O(n3)与 16n4 +O(n3)之间 。

This paper proves \$∫\+1\-\{-1\}|f′(x)|\+2\%d\%x≤124(n+1)(2n+1)(2n\+2+7n+3)∫\+1\-\{-1\}|f(x)|\+2\%d\%x\$ for all \%f(x)∈P\-n\%,where \%P\-n\% denotes the set of all algebraic polynomials of degree at most \%n\%. The left best possible constants is between \%110n\+4+O(n\+3)16n\+4+O(n\+3)\%. An error in the preceding paper is emended.