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<p>We prove two-weight norm inequalities for parabolic fractional maximal functions using parabolic Muckenhoupt weights. In particular, we prove a two-weight, weak-type estimate and Fefferman–Stein type inequalities for the centered parabolic maximal function. We also prove that a parabolic Sawyer-type condition implies the strong-type estimate for the parabolic fractional maximal function. Finally, we prove the strong-type estimate for the centered parabolic maximal function assuming a stronger parabolic Muckenhoupt bump condition.</p>

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Two-weight norm inequalities for parabolic fractional maximal functions

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  • 出版模式：

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  • 发表日期：

    2025年11月22日

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  • David Cruz-Uribe,
  • Kim Myyryläinen

摘要

We prove two-weight norm inequalities for parabolic fractional maximal functions using parabolic Muckenhoupt weights. In particular, we prove a two-weight, weak-type estimate and Fefferman–Stein type inequalities for the centered parabolic maximal function. We also prove that a parabolic Sawyer-type condition implies the strong-type estimate for the parabolic fractional maximal function. Finally, we prove the strong-type estimate for the centered parabolic maximal function assuming a stronger parabolic Muckenhoupt bump condition.