Cantor集上的对数Sobolev不等式

LOGARITHMIC SOBOLEV INEQUALITY ON CANTOR SETS

利用两点不等式和构造一类特殊的映射的方法，证明了一类特殊集合—Cantor集上的标准Laplace算子满足对数Sobolev不等式，并给出相应的对数Sobolev常数的估计．

Logarithmic Sobolev inequality is proved to hold for the standard Laplace on Cantor sets through two- point inequality and construction of a series of maps, and then the log- Sobolev constant is given.