Some capacitary strong type inequalities and related function spaces
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914085893832704 |
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| author | Ooi, Keng Hao Phuc, Nguyen Cong |
| author_facet | Ooi, Keng Hao Phuc, Nguyen Cong |
| contents | We verify a conjecture of D. R. Adams on a capacitary strong type inequality that generalizes the classical capacitary strong type inequality of V. G. Maz'ya. As a result, we characterize related function spaces as Köthe duals to a class of Sobolev multiplier type spaces. Moreover, using tools from nonlinear potential theory, weighted norm inequalities, and Banach function space theory, we show that these spaces are also isomorphic to more concrete spaces that are easy to use and fit in well with the modern theory of function spaces of harmonic analysis. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_08982 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some capacitary strong type inequalities and related function spaces Ooi, Keng Hao Phuc, Nguyen Cong Classical Analysis and ODEs Analysis of PDEs Functional Analysis We verify a conjecture of D. R. Adams on a capacitary strong type inequality that generalizes the classical capacitary strong type inequality of V. G. Maz'ya. As a result, we characterize related function spaces as Köthe duals to a class of Sobolev multiplier type spaces. Moreover, using tools from nonlinear potential theory, weighted norm inequalities, and Banach function space theory, we show that these spaces are also isomorphic to more concrete spaces that are easy to use and fit in well with the modern theory of function spaces of harmonic analysis. |
| title | Some capacitary strong type inequalities and related function spaces |
| topic | Classical Analysis and ODEs Analysis of PDEs Functional Analysis |
| url | https://arxiv.org/abs/2510.08982 |