球面上Peetre　K－模和最佳逼近

The Peetre K-Moduli and Best Approximation on the Sphere

本文研究了球面上三种ＰｅｅｔｒｅＫ－模与最佳逼近的关系，建立起它们之间的若干强型和弱型不等式．此外，还讨论了Ｋ－模与光滑模的等价性．

There are various ways to describe the smoothness of functions on the sphere and,consequently, the best approximation may be estimated by different moduli of smoothness. An-other powerful modulus is Peetre’s K-modulus.Indeed, for functions on the sphere the Peetre K-moduli seem to be easier to handle. The aim of the paper is to present relationships between different K-moduli and best approximation, and to show that Peetre’s modulus is , in general, equivalent to a suitable modulus of smoothness.