Parabolic weak porosity and parabolic Muckenhoupt distance functions
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908962709831680 |
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| author | Lahdelma, Henri Myyryläinen, Kim Vähäkangas, Antti V. |
| author_facet | Lahdelma, Henri Myyryläinen, Kim Vähäkangas, Antti V. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_12561 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Parabolic weak porosity and parabolic Muckenhoupt distance functions Lahdelma, Henri Myyryläinen, Kim Vähäkangas, Antti V. Classical Analysis and ODEs Analysis of PDEs 42B35, 42B37, 28A75, 28A80 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. |
| title | Parabolic weak porosity and parabolic Muckenhoupt distance functions |
| topic | Classical Analysis and ODEs Analysis of PDEs 42B35, 42B37, 28A75, 28A80 |
| url | https://arxiv.org/abs/2604.12561 |