论文标题
关于$ k $功能，平滑模量，杰克逊定理和尼古斯基 - 斯蒂奇金的不平等现象
A note on $K$-functional, Modulus of smoothness, Jackson theorem and Nikolskii-Stechkin inequality on Damek-Ricci spaces
论文作者
论文摘要
在本文中，我们研究了damek-ricci空间上的$ l^2 $空间的近似定理。我们证明了使用damek-Icci空间上的球形平均操作员定义的平滑度模量的近似值的直接杰克逊定理。我们还证明了Nikolskii-Stechkin不平等。为了证明这些不平等现象，我们使用有界频谱的函数作为近似工具。最后，作为一个应用程序，我们证明了damek-ricci空间的$ k $功能和模量的等效性。
In this paper we study approximation theorems for $L^2$-space on Damek-Ricci spaces. We prove direct Jackson theorem of approximations for the modulus of smoothness defined using spherical mean operator on Damek-Ricci spaces. We also prove Nikolskii-Stechkin inequality. To prove these inequalities we use functions of bounded spectrum as a tool of approximation. Finally, as an application, we prove equivalence of the $K$-functional and modulus of smoothness for Damek-Ricci spaces.
