Functions of bounded variation, the derivative of the one dimensional maximal function, and applications to inequalities
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- by J. M. Aldaz and J. Pérez Lázaro PDF
- Trans. Amer. Math. Soc. 359 (2007), 2443-2461 Request permission
Abstract:
We prove that if $f:I\subset \mathbb {R}\to \mathbb {R}$ is of bounded variation, then the uncentered maximal function $Mf$ is absolutely continuous, and its derivative satisfies the sharp inequality $\|DMf\|_{L^1(I)}\le |Df|(I)$. This allows us to obtain, under less regularity, versions of classical inequalities involving derivatives.References
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Additional Information
- J. M. Aldaz
- Affiliation: Departamento de Matemáticas y Computación, Universidad de La Rioja, 26004 Logroño, La Rioja, Spain
- Email: aldaz@dmc.unirioja.es
- J. Pérez Lázaro
- Affiliation: Departamento de Matemáticas e Informática, Universidad de La Rioja, 26004 Logroño, La Rioja, Spain
- Email: javier.perezl@unirioja.es
- Received by editor(s): December 30, 2005
- Published electronically: December 19, 2006
- Additional Notes: The authors were partially supported by Grant BFM2003-06335-C03-03 of the D.G.I. of Spain
The second author thanks the University of La Rioja for its hospitality. - © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 359 (2007), 2443-2461
- MSC (2000): Primary 42B25, 26A84
- DOI: https://doi.org/10.1090/S0002-9947-06-04347-9
- MathSciNet review: 2276629