Functions of bounded variation, the derivative of the one dimensional maximal function, and applications to inequalities
Functions of bounded variation, the derivative of the one dimensional maximal function, and applications to inequalities
复制标题
DOI：
10.1090/s0002-9947-06-04347-9
复制
发表时间：
2006-01
影响因子：
1.3
通讯作者：
J. M. Aldaz;J. Lázaro
中科院分区：
文献类型：
--
作者：
J. M. Aldaz;J. Lázaro
证明了如果f：i⊂R→R是有界变差的，则非中心极大函数Mf是绝对连续的，且它的导数满足∥dmf∥L 1(I)<；|df|(I).这使得我们可以在较少的正则性下获得涉及导数的经典不等式的版本。
We prove that if f: I ⊂ R→ R is of bounded variation, then the uncentered maximal function Mf is absolutely continuous, and its derivative satisfies the sharp inequality ∥DMf∥ L 1(I) < |Df|(I). This allows us to obtain, under less regularity, versions of classical inequalities involving derivatives.