度量空间粗嵌入进l_2的一个注记

On the Coarse Embeddability of l_p-Spaces Into l_2

对l(_p-)空间与l_2之间粗嵌入关系作进一步的研究,证明了度量空间X可粗嵌入进l_2当且仅当存在某个2<P_0<∞,使得X可一致地粗嵌入进{l_p,2<P≤p_0}.这给出度量空间粗嵌入进l_2的一个等价刻画.

We made some further research on the coarse embeddability between lpspaces and l2 and we proved that a metric space X can be coarsely embedded into 12 if and only if there exists some P0 〉 0 such that X can be coarsely embedded into {lp, 2 〈 p≤ P0} uniformly. This gave an equivalent condition for the coarse embeddability of metric spaces into 12.