某可微函数类在Orlicz空间内的宽度估计

On $n$-Widths of Certain Function Classes in Orlicz Spaces

中文关键词:  Orlicz空间  样条类  函数类  宽度  对偶.

英文关键词:Orlicz space  spline class  function class  width  duality.

中文摘要:

      本文首先研究了$r$阶广义样条类在Orlicz空间内的极值问题,由此进一步 考虑了光滑函数类$\Omega_{\infty}^{r}[0,1]$在Orlicz空间内的$n$宽度的 精确估计问题.最后还讨论了相应的对偶情形.

英文摘要:

      This paper deals with the extremal problems of general spline classes which degree of \emph{r} in Orlicz spaces. Based on this, we further study the problems of precisely estimation on $n$-Widths of smoothness function classes $\Omega_{\infty}^{r}[0,1]$ in Orlicz spaces. Moreover, we discuss the problems of corresponding dual cases.