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 o...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.展开更多
In this paper, we study the intersection of Mcmullen set with its rational translation. The main difficulty is that the generating structure of the intersection. By the radix expansion of translating vector, we give i...In this paper, we study the intersection of Mcmullen set with its rational translation. The main difficulty is that the generating structure of the intersection. By the radix expansion of translating vector, we give its fractal characterization. We find that the Hausdorff measure of these sets forms a discrete spectrum whose non-zero values come only from translating the vector （x,y） with its radix expansion.展开更多
基金supported by National Natural Science Foundation of China (Grant Nos.10971056,10771164)
文摘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 the National Science Foundation of China (10671180) and Jiangsu University (05JDG041)
文摘In this paper, we study the intersection of Mcmullen set with its rational translation. The main difficulty is that the generating structure of the intersection. By the radix expansion of translating vector, we give its fractal characterization. We find that the Hausdorff measure of these sets forms a discrete spectrum whose non-zero values come only from translating the vector （x,y） with its radix expansion.
