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<p>Given a measure space with a ball-basis, we introduce a class of global log-Hölder continuity conditions for variable exponent functions, and we show that the Hardy-Littlewood maximal operator is bounded on weighted variable Lebesgue spaces if and only if the weights satisfy the variable Muckenhoupt condition. As an application, in virtue of extrapolation we establish the weighted norm inequalities for a class of bounded oscillation operators on these variable Lebesgue spaces.</p>

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Weighted variable Lebesgue spaces and abstract measure spaces

  • 期刊论文

  • 发表日期：

    2026年5月9日

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  • Songbai Wang,
  • Haiyan Zhou,
  • Jiang Zhou

摘要

Given a measure space with a ball-basis, we introduce a class of global log-Hölder continuity conditions for variable exponent functions, and we show that the Hardy-Littlewood maximal operator is bounded on weighted variable Lebesgue spaces if and only if the weights satisfy the variable Muckenhoupt condition. As an application, in virtue of extrapolation we establish the weighted norm inequalities for a class of bounded oscillation operators on these variable Lebesgue spaces.