Orlicz空间内一类有理函数逼近的一种Jackson型估计

A Jackson type estimator for a class of rational function approximation in Orlicz spaces

研究了Orlicz空间内一类有理函数逼近问题.在被逼近函数改变l次符号的条件下,借助Steklov平均函数,利用修正的Jackson核,Hardy-Littlewood极大函数,Cauchy-Schwarz不等式等工具,给出了逼近阶的一种Jackson型估计.考虑到Orlicz空间内拓扑结构的复杂性,本文得到的结果比连续函数空间和L_p空间内同类问题的研究结果具有更广泛的意义.

It studies the approximation in Orlicz spaces for a class of rational function.under the condition of approximationed function changed l sub-symbols,with average Steklov function,using the modified Jackson kernel,Hardy-Littlewood maximal function,Cauchy-Schwarz inequality and other tools,we estimate a Jackson type approximation.Considering the complexity of topological structure in Orlicz spaces,the results obtained in this paper are more extensive than those of the continuous function spaces and the similar problems in Lp spaces.