Lagrange插值和Hermite插值在Orlicz空间内的逼近

Lagrange Interpolation and Hermite Interpolation Approximation in Orlicz Spaces

在Orlicz空间内研究问题是函数逼近论研究方向里的重要分支之一.插值逼近问题有着深远的理论意义和广泛的应用前景.本文在连续函数空间和L_p空间内研究插值逼近方法的基础上,研究一种Lagrange线性组合插值算子和Hermite插值算子在Orlicz空间内的逼近问题,利用连续模,Holder等式,Hardy-Littlewood极大函数,给出两类插值的逼近度估计,所得的结果更精确于前人的同类结果.

For researching in the Orlicz space is an important branch of research in the function approximation theory. It has far-reaching theoretical significance and wide application prospect of interpolation approximation problem. Based on interpolation approximation method in continuous function space and space, this paper studies the approximation problems of a linear combination of Lagrange interpolation algorithm and Hermite interpolation operator in Orlicz space. Two kinds of interpolation is given by using the continuous mode, Holder inequality, Hardy-Littlewood maximal function, estimation of approximation degree. The more accurate the results are obtained from previous similar results.