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.