中文摘要：

函数的最优恢复问题是计算复杂性的重要组成部分，而Levy平均估计式是研究最优恢复问题的重要工具。给出了Lp（0〈p〈∞）空间中Levy平均的一个等价估计式，并将此估计式应用到球面多项式空间中，发现在满足一定的条件下，存在一个球调和函数，使得当2〈p〈∞时该函数的P范数与2数范等价。

英文摘要：

The theory of optimal reconstruction is an important part of computational complexity,and the estimations of Levy mean are widely used in the study of the optimal recovery problems. An important estimation of Levy mean in Lp spaces with 0 p ∞ was obtained. As an application of this result on the space of spherical polynomials,there exists a spherical polynomial such that the norms are equivalent for 2≤p ∞ under some conditions.