International Journal of Mathematics and Mathematical Sciences
Volume 32 (2002), Issue 2, Pages 65-71
doi: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 Huang Xinzhong et al. 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
ℝ with the properties f(0)=f(1)=0 and that ‖f‖ z =infx,t|f(x+t)−2f(x)+f(x−t)/t|is finite for all x,t∈ℝ, which is called Zygmund function on ℝ, then maxx∈[0,1]|f(x)|≤(11/32)‖f‖z. As an
application, we obtain a better estimate for Skedwed Zygmund
bound in Zygmund class.