Orlicz空间中的多元光滑模及其应用(英文)

Multivariate Modulus of Smoothness in Orlicz Spaces and Its Application

本文的目的是引进和应用Orlicz空间中一种新的多元光滑模,该光滑模是一元情形的一种自然推广。利用函数分解方法和归纳讨论证明它与K-泛函之间的等价关系。作为应用,给出定义在单纯形上Durrmeyer算子在Orlicz空间中的一个逼近逆定理。

The aim of this paper is to introduce and apply a new multivariate modulus of smoothness in Orlicz spaces, which generalizes the one for single variable in a natural way. The equivalent relationship between the modulus and some K-functional is shown by using an induction argument and a decomposition technique. As an application for the modulus, an inverse theorem of approximation on the multivariate Durrmeyer operators in Rd is given.