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Abstract <p> We find exact orders of decrease of quantities that characterize various properties of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(2\pi\)</EquationSource> </InlineEquation>-periodic summable functions on a class with given majorant of the second-order modulus of continuity. We show that all these quantities have the same order of decrease (with a single condition on the behavior of the majorant), which is attained on a singe extremal function. </p>

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On an Extremal Gheit Function and Its Applications

  • 期刊论文

  • 发表日期：

    2026年3月27日

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  • N.A. Ilyasov,
  • A.R. Alimov

摘要

Abstract

We find exact orders of decrease of quantities that characterize various properties of \(2\pi\) -periodic summable functions on a class with given majorant of the second-order modulus of continuity. We show that all these quantities have the same order of decrease (with a single condition on the behavior of the majorant), which is attained on a singe extremal function.