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International Journal of Mathematics and Mathematical Sciences
Volume 32, Issue 2, Pages 65-71
http://dx.doi.org/10.1155/S0161171202202306

On the maximum value for Zygmund class on an interval

1Department of Applied Mathematics, Huaqiao National University, Quanzhou, Fujian 362011, China
2Department of Mathematics, Kyungsung University, Pusan 608-736, China

Received 2 February 2002

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We prove that if f(z) is a continuous real-valued function on with the properties f(0)=f(1)=0 and that fz=infx,t|f(x+t)2f(x)+f(xt)/t|is finite for all x,t, which is called Zygmund function on , then maxx[0,1]|f(x)|(11/32)fz. As an application, we obtain a better estimate for Skedwed Zygmund bound in Zygmund class.