Fatness and thinness of uniform Cantor sets for doubling measures  

作　　者：PENG FengJi WEN ShengYou 

机构地区：[1]Department of Mathematics, South China University of Technology, Guangzhou 510641, China [2]Department of Mathematics, Hubei University, Wuhan 430062, China

出　　处：《Science China Mathematics》2011年第1期75-81,共7页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant Nos.10971056,10771164)

摘　　要：Let E = E({nk},{ck}) be a fat uniform Cantor set. We prove that E is a minimally fat set for doubling measures if and only if (nkck)p = ∞ for all p < 1 and that E is a fairly fat set for doubling measures if and only if there are constants 0 < p < q < 1 such that (nkck)q < ∞ and (nkck)p = ∞. The classes of minimally thin uniform Cantor sets and of fairly thin uniform Cantor sets are also characterized.Let E = E（{nk},{ck}） be a fat uniform Cantor set. We prove that E is a minimally fat set for doubling measures if and only if （nkck）p = ∞ for all p 〈 1 and that E is a fairly fat set for doubling measures if and only if there are constants 0 〈 p 〈 q 〈 1 such that （nkck）q 〈 ∞ and （nkck）p = ∞. The classes of minimally thin uniform Cantor sets and of fairly thin uniform Cantor sets are also characterized.

关 键 词：uniform Cantor set doubling measure minimally fat fairly fat minimally thin fairly thin 

分 类 号：O174.1[理学—数学] O174.12[理学—基础数学]