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2002-2003 An estimate of the first derivative by the Laplacian.
Roman Dwilewicz
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Real Anal. Exchange 28(1): 145-152 (2002-2003).


In this note a particular case of the following general problem is considered: how to control lower order derivatives by higher ones, at least over a sequence of points. The following particular case is proved: if a $C^2$ negative-valued function $h=h(w)$ depends on one complex variable in the unit disc and $h(1)=h_w(1)=0$, then the first derivative $h_w$ is controlled by the Laplacian of $h$ over a sequence of points converging to $w=1$. Such kind of estimates have applications to delicate problems of convexity with respect to various families of functions.


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Roman Dwilewicz. "An estimate of the first derivative by the Laplacian.." Real Anal. Exchange 28 (1) 145 - 152, 2002-2003.


Published: 2002-2003
First available in Project Euclid: 12 June 2006

zbMATH: 1059.31001
MathSciNet: MR1973975

Primary: 26B25
Secondary: 31A05 , 32F05 , 52A41

Keywords: Laplacian , real functions

Rights: Copyright © 2002 Michigan State University Press

Vol.28 • No. 1 • 2002-2003
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