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Abstract <p> We obtain an improvement of the John–Nirenberg inequality for the series of the form <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11006_2025_3017_Article_IEq1.gif" Format="GIF" Height="21" Rendition="HTML" Resolution="72" Type="Linedraw" Width="161" /> </InlineMediaObject> <EquationSource Format="TEX">\(\sum_{n=1}^{\infty}n^{-1}\exp(2\pi i n^k x)\)</EquationSource> </InlineEquation>, <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11006_2025_3017_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="42" /> </InlineMediaObject> <EquationSource Format="TEX">\(k&gt;2\)</EquationSource> </InlineEquation>, on intervals consisting of points with the same convergent of continued fractions. We also establish a convergence criterion for these series. </p>

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John–Nirenberg Inequality for Riemann Type Series

  • 期刊论文

  • 发表日期：

    2025年2月1日

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  • K. A. Oganesyan

摘要

Abstract

We obtain an improvement of the John–Nirenberg inequality for the series of the form \(\sum_{n=1}^{\infty}n^{-1}\exp(2\pi i n^k x)\) , \(k>2\) , on intervals consisting of points with the same convergent of continued fractions. We also establish a convergence criterion for these series.