On Quantitative Sphere Equivalence and Extrapolation Phenomenon  

作　　者：Jun Xi CHEN Qing Jin CHENG 

机构地区：[1]School of Mathematical Sciences,Xiamen University,Xiamen 361005,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2022年第4期709-717,共9页数学学报（英文版）

基　　金：NSFC(Grant Nos.12071389,11731010 and 12026237)。

摘　　要：Let X,Y be Banach spaces.We prove that if their unit spheres S(X)and S(Y)are(α,β)-Hlder homeomorphic for someα,β∈(0,1].Then the unit spheres of Lp[Ω,μ,X)and Lq(Ω,μ,Y)are(min{p/q,α},min{q/p,β})-Hlder homeomorphic for every measure space(Ω,μ)and for every 1≤p,q<∞.In particular,the result yields an interesting application involving extrapolation phenomenon.

关 键 词：Banach space Hlder equivalence unit sphere Matouek’s extrapolation phenomenon 

分 类 号：O177.2[理学—数学]