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.
基金
supported by National Natural Science Foundation of China (Grant Nos.10971056,10771164)
关键词
CANTOR集
均匀康托集
消瘦
肥胖
NK细胞
脂肪
芘
uniform Cantor set, doubling measure, minimally fat, fairly fat, minimally thin, fairly thin
