论文标题
关于BV函数的最大函数的规律性
On the regularity of the maximal function of a BV function
论文作者
论文摘要
我们表明，BV函数的非中心最大函数是错误的。我们还表明，\ emph {if} SBV函数的非中心最大函数是BV函数，实际上它是Sobolev函数。使用WEIGT的最新结果，我们特别能够证明一组有限周长的非中心最大函数是Sobolev函数。
We show that the non-centered maximal function of a BV function is quasicontinuous. We also show that \emph{if} the non-centered maximal functions of an SBV function is a BV function, then it is in fact a Sobolev function. Using a recent result of Weigt, we are in particular able to show that the non-centered maximal function of a set of finite perimeter is a Sobolev function.
