单位球面上的一极值问题(英文)

An Extremal Problem on Unit Sphere

设Ω是R^n中的紧集,1<p≤∞。是n+1个线性独立元素,其线性包是n+1维子空间E.令(y_0,…,y_n)∈R^(n+1),y_i≥0(i=0,…,n).本文考虑极值问题不失一般性,我们只须考虑这里0≤S≤n是一确定的整数,得到了K的估计.

Let Ω be a compact set in R^n, {f_i}_i^n=0 L^p(Ω), 1<p ≤∞ be n+1 linearly independent elements Which span the (n+1)dimensional subspace E. Let (y_o,…, y_n)∈R^(n+1), y_i≥0,i=0,…,n. In this paper we consider the following extremal problem Without loss of generality, we need only to consider the problem where 0≤s≤n is a fixed integer and obtain the estimation for K.