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2003-2004 On pointwise Hölder functions.
E. D'Aniello, P. de Lucia
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Real Anal. Exchange 29(2): 713-728 (2003-2004).


Let $f: X \rightarrow {\mathbb R}$, where $X$ is a subset of ${\mathbb R}^{k}$. We observe that in order for $f$ be almost everywhere pointwise Hölder it is enough that $f$ satisfy the Hölder condition inside angles of a fixed width. In this analysis, density points of $X$ play a primary role. This has some interesting consequences concerning summability of a naturally defined coefficient.


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E. D'Aniello. P. de Lucia. "On pointwise Hölder functions.." Real Anal. Exchange 29 (2) 713 - 728, 2003-2004.


Published: 2003-2004
First available in Project Euclid: 7 June 2006

zbMATH: 1102.26010
MathSciNet: MR2083807

Primary: 26B35
Secondary: 28A20

Keywords: Lipschitz functions , parameter of regularity

Rights: Copyright © 2003 Michigan State University Press

Vol.29 • No. 2 • 2003-2004
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