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
Huang Xinzhong1
, Oh Sang Kwon2
and Jun Eak Park2
1Department of Applied Mathematics, Huaqiao National University, Quanzhou, Fujian 362011, China
2Department of Mathematics, Kyungsung University, Pusan 608-736, China
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.