One-sided median porosity of E is necessary and sufficient for d_E to the minus alpha to be in one-sided A_p for some alpha greater than zero when 1 less than p less than infinity, with new median characterizations of A_p and BMO.
Parabolic weak porosity and parabolic Muckenhoupt distance functions
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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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math.CA 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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One-sided median porous sets and one-sided Muckenhoupt distance functions
One-sided median porosity of E is necessary and sufficient for d_E to the minus alpha to be in one-sided A_p for some alpha greater than zero when 1 less than p less than infinity, with new median characterizations of A_p and BMO.