Functions of bounded variation, the derivative of the one dimensional maximal function, and applications to inequalities期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Functions of bounded variation, the derivative of the one dimensional maximal function, and applications to inequalities

Authors:	J. M. Aldaz J. Pé rez Lá zaro

Affiliation:	Departamento de Matemáticas y Computación, Universidad de La Rioja, 26004 Logroño, La Rioja, Spain ; Departamento de Matemáticas e Informática, Universidad de La Rioja, 26004 Logroño, La Rioja, Spain

Abstract:	We prove that if is of bounded variation, then the uncentered maximal function is absolutely continuous, and its derivative satisfies the sharp inequality $Vert DMfVert _{L^1(I)}le vert Dfvert(I)$ . This allows us to obtain, under less regularity, versions of classical inequalities involving derivatives.

Keywords:	Maximal function functions of bounded variation.

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