An Estimate of the First Derivative by the Laplacian
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 C2 negative-valued function h=h(w) depends on one complex variable in the unit disc and h(1)=hw(1)=0, then the first derivative hw 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.
R. Dwilewicz, "An Estimate of the First Derivative by the Laplacian," Real Analysis Exchange, Real Analysis Exchange, Jan 2002.
Mathematics and Statistics
Keywords and Phrases
real functions; Laplacian
Article - Journal
© 2002 Real Analysis Exchange, All rights reserved.
01 Jan 2002