Jordan区域上多项式不等式与插值

On the Inequality of Polynomials and Interpolation in a Jordan Domain

本文在Jordan区域上得到一个多项式在区域边界上的L^p范数(P>1),被其Fejer插值点上的函数值及其导数值所控制的不等式。此外,用这个不等式,再一次地得到函数的Hermite-Fejer插值多项式在L^p(Γ),0<P<+∞,上逼近函数时的阶的估计。

In this paper we obtained an inequality which shows that the norm of polynomials in Lp(Γ), p>1, are dominanted by its values and derivatives at the Fejers points in a Jordan domain D, where Γ is the boundary of D. Besides, using this inequality the degree of approximation in Lp(Γ), 0<p<+∞, of functions of class A(D) by Her-mite-Fejer interpolation polynomials is presented again.