On the maximum value for Zygmund class on an interval

Huang Xinzhong, Oh Sang Kwon and Jun Eak Park

International Journal of Mathematics and Mathematical Sciences, 2002, vol. 32, 1-7

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 = inf x , t | f ( x + t ) − 2 f ( x ) + f ( x − t ) / t | is finite for all x , t ∈ ℝ , which is called Zygmund function on ℝ , then max x ∈ [ 0 , 1 ] | f ( x ) | ≤ ( 11 / 32 ) ‖ f ‖ z . As an application, we obtain a better estimate for Skedwed Zygmund bound in Zygmund class.

Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:329498

DOI: 10.1155/S0161171202202306

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