Orlicz空间内的Muntz有理函数的逼近

Rational Approximation of Muntz in Orlicz Spaces

本文研究了Orlicz空间内Muntz有理函数逼近问题,相比于前人对同类问题的研究,本文改进了系指数{λn}n^∞=1所满足的条件,利用Holder不等式、Hardy-Littlewood极大函数、K-泛函、连续模、N函数的凸性等技巧,得到逼近的Jackson型定理.由于Orlicz空间的拓扑结构比连续函数空间和Lp空间复杂,所以本文的结果具有一定的拓展意义.

In this paper,we study Muntz rational approximation problems in Orlicz spaces,compare with previous studies on similar problems and tries to improve the index {λn}n^∞=1 meet the conditions.Using the Holder inequality,Hardy-Littlewoods maximal function,K-functional continuous modulus and convexity of N-function techniques,the Jackson type theorem of approximation is obtained.Since Orlicz space’s topological structure is more complex than continuous function space and Lp spaces,the results of this paper have certain expansion significance.