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arXiv · 2604.12561

Parabolic weak porosity and parabolic Muckenhoupt distance functions

Henri Lahdelma·Kim Myyryläinen·Antti V. Vähäkangas
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Abstract

We develop the parabolic weak porosity to characterize the parabolic Muckenhoupt $A_1$ weights with time-lag. Our main result shows that a nonempty closed set is parabolic weakly porous if and only if the parabolic distance function of the set to a negative power is in the parabolic Muckenhoupt $A_1$ class. We apply a novel stopping time argument in combination with the translation and doubling results for the parabolic weakly porous sets.

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Henri Lahdelma, Kim Myyryläinen, Antti V. Vähäkangas. 2026-04-14. Parabolic weak porosity and parabolic Muckenhoupt distance functions. https://arxiv.org/abs/2604.12561

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