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2004-2005 An Lp differentiable non-differentiable function.
J. Marshall Ash
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Real Anal. Exchange 30(2): 747-754 (2004-2005).


There is a set $E$ of positive Lebesgue measure and a function nowhere differentiable on $E$ which is differentiable in the $L^p$ sense for every positive $p$ at each point of $E$. For every $p\in(0,\infty]$ and every positive integer $k$ there is a set $E=E(k,p)$ of positive measure and a function which for every $q< p$ has $k$ $L^q$ Peano derivatives at every point of $E$ despite not having an $L^p$ $k$th derivative at any point of $E$.


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J. Marshall Ash. "An Lp differentiable non-differentiable function.." Real Anal. Exchange 30 (2) 747 - 754, 2004-2005.


Published: 2004-2005
First available in Project Euclid: 15 October 2005

MathSciNet: MR2177431

Primary: 26A27
Secondary: 26A24

Keywords: $L^{p}$ derivative , $L^{p}$ Peano derivative , Peano derivative , super density

Rights: Copyright © 2004 Michigan State University Press

Vol.30 • No. 2 • 2004-2005
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