The Capacitary John-Nirenberg Inequality Revisited
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909758908268544 |
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| author | Basak, Riju Chen, You-Wei Benson Roychowdhury, Prasun Spector, Daniel |
| author_facet | Basak, Riju Chen, You-Wei Benson Roychowdhury, Prasun Spector, Daniel |
| contents | In this paper, we establish maximal function estimates, Lebesgue differentiation theory, Calderón-Zygmund decompositions, and John-Nirenberg inequalities for translation invariant Hausdorff contents. We further identify a key structural component of these results -- a packing condition satisfied by these Hausdorff contents which compensates for the non-linearity of the capacitary integrals. We prove that for any outer capacity, this packing condition is satisfied if and only if the capacity is equivalent to its induced Hausdorff content. Finally, we use this equivalence to extend the preceding theory to general outer capacities which are assumed to satisfy this packing condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_11412 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Capacitary John-Nirenberg Inequality Revisited Basak, Riju Chen, You-Wei Benson Roychowdhury, Prasun Spector, Daniel Functional Analysis Analysis of PDEs In this paper, we establish maximal function estimates, Lebesgue differentiation theory, Calderón-Zygmund decompositions, and John-Nirenberg inequalities for translation invariant Hausdorff contents. We further identify a key structural component of these results -- a packing condition satisfied by these Hausdorff contents which compensates for the non-linearity of the capacitary integrals. We prove that for any outer capacity, this packing condition is satisfied if and only if the capacity is equivalent to its induced Hausdorff content. Finally, we use this equivalence to extend the preceding theory to general outer capacities which are assumed to satisfy this packing condition. |
| title | The Capacitary John-Nirenberg Inequality Revisited |
| topic | Functional Analysis Analysis of PDEs |
| url | https://arxiv.org/abs/2501.11412 |