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arXiv · 2306.07600

Characterizations of parabolic Muckenhoupt classes

Juha Kinnunen·Kim Myyryläinen
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Abstract

This paper extends and complements the existing theory for the parabolic Muckenhoupt weights motivated by one-sided maximal functions and a doubly nonlinear parabolic partial differential equation of $p$-Laplace type. The main results include characterizations for the limiting parabolic $A_\infty$ and $A_1$ classes by applying an uncentered parabolic maximal function with a time lag. Several parabolic Calder\'on-Zygmund decompositions, covering and chaining arguments appear in the proofs.

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Juha Kinnunen, Kim Myyryläinen. 2023-06-13. Characterizations of parabolic Muckenhoupt classes. https://arxiv.org/abs/2306.07600

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