On the maximum value for Zygmund class on an interval

Xinzhong, Huang; Kwon, Oh Sang; Park, Jun Eak

doi:https://doi.org/10.1155/S0161171202202306

International Journal of Mathematics and Mathematical Sciences

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Volume 32 |Article ID 329498 | https://doi.org/10.1155/S0161171202202306

Huang Xinzhong, Oh Sang Kwon, Jun Eak Park, "On the maximum value for Zygmund class on an interval", International Journal of Mathematics and Mathematical Sciences, vol. 32, Article ID 329498, 7 pages, 2002. https://doi.org/10.1155/S0161171202202306

On the maximum value for Zygmund class on an interval

Huang Xinzhong,¹ Oh Sang Kwon,² and Jun Eak Park²

¹Department of Applied Mathematics, Huaqiao National University, Quanzhou, Fujian 362011, China

²Department of Mathematics, Kyungsung University, Pusan 608-736, China

Received02 Feb 2002

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.

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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.

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