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<p>Sufficient conditions for the uniform boundedness of the Steklov averaging operators in weighted variable exponent spaces of periodic functions are obtained.The boundedness of the Steklov averages was previously known if the exponent satisfies the Dini-Lipschitz condition and a local analogue of the Muckenhoupt condition holds. In this paper, the boundedness of the Steklov averages is established under certain Muckenhoupt type conditions solely, and the Dini-Lipschitz condition is not required. The norms of averaging operators are estimated explicitly.</p>

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Boundedness of averaging operators in weighted variable exponent spaces of periodic functions

  • 期刊论文

  • 发表日期：

    2025年4月22日

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  • O. L. Vinogradov

摘要

Sufficient conditions for the uniform boundedness of the Steklov averaging operators in weighted variable exponent spaces of periodic functions are obtained.The boundedness of the Steklov averages was previously known if the exponent satisfies the Dini-Lipschitz condition and a local analogue of the Muckenhoupt condition holds. In this paper, the boundedness of the Steklov averages is established under certain Muckenhoupt type conditions solely, and the Dini-Lipschitz condition is not required. The norms of averaging operators are estimated explicitly.