The findings demonstrate two-weight norm inequalities and estimates in parabolic functions, suggesting implications for mathematical analysis.
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.
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Cruz-Uribe et al. (2025) studied this question.
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