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<p>A criterion for the uniform boundedness of Steklov averaging operators in variable exponent spaces of periodic functions is obtained. This criterion coincides with the known local analog of the Muckenhoupt condition. The boundedness of Steklov averages was previously known under the Dini–Lipschitz condition. The norms of averaging operators are estimated explicitly. Bibliography: 19 titles.</p>

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A BOUNDEDNESS CRITERION FOR AVERAGING OPERATORS IN VARIABLE EXPONENT SPACES OF PERIODIC FUNCTIONS

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • O. L. Vinogradov

摘要

A criterion for the uniform boundedness of Steklov averaging operators in variable exponent spaces of periodic functions is obtained. This criterion coincides with the known local analog of the Muckenhoupt condition. The boundedness of Steklov averages was previously known under the Dini–Lipschitz condition. The norms of averaging operators are estimated explicitly. Bibliography: 19 titles.