用平均连续模给出渐近Fejér点组上插值算子的平均逼近阶

Order of Approximation in the Mean by Interpolatory Operators at Nearly Fejer Nodes Using Average Modulas of Continuity

本文在对区域D的边界Γ作了较弱的光滑性假设下,得到了用平均连续模来刻划D内有界解析,在Γ上Riemann可积函数在渐近Fej(?)r点组上的Lagrange及Hermite-Fej(?)r插值算子在L^P(Γ),P>1意义下逼近函数的平均逼近阶,在得到这些估计式时,我们首先在一般区域上,对渐近Fej(?)r点组,导出了Marcinkiewicz-Zygmund型不等式。

Under certain mild condition on the smoothness of the boundary Γ of a domain D, the order of approximation in the mean is obtained by Lagrange and Hermite-Fejer in terpolating polynomials at the nearly Fejer node for the class Hc (D) of functions bounded analytic and Riemann integrable on Γ using average modulus of Continuity, In establishing our estimates,we have also derived some Marcinkiewicz-Zygmund typed inequality for nearly Fejer nodes.