Capacity and Hausdorff measure in Musielak-Orlicz-Sobolev spaces
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866913739271307264 |
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| author | Pandey, Ankur Karak, Nijjwal Mondal, Debarati |
| author_facet | Pandey, Ankur Karak, Nijjwal Mondal, Debarati |
| contents | In this paper, we show that sets with zero Sobolev $p(\cdot)$-capacity have generalized Hausdorff $h(\cdot)$-measure zero, for some gauge function $h(\cdot).$ We also prove that sets with zero Musielak-Orlicz-Sobolev $Φ(\cdot,\cdot)$-capacity, for a particular class of functions $Φ(\cdot,\cdot),$ have generalized Hausdorff $h(\cdot)$-measure zero, for a suitable gauge function $h(\cdot).$ |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_12849 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Capacity and Hausdorff measure in Musielak-Orlicz-Sobolev spaces Pandey, Ankur Karak, Nijjwal Mondal, Debarati Functional Analysis In this paper, we show that sets with zero Sobolev $p(\cdot)$-capacity have generalized Hausdorff $h(\cdot)$-measure zero, for some gauge function $h(\cdot).$ We also prove that sets with zero Musielak-Orlicz-Sobolev $Φ(\cdot,\cdot)$-capacity, for a particular class of functions $Φ(\cdot,\cdot),$ have generalized Hausdorff $h(\cdot)$-measure zero, for a suitable gauge function $h(\cdot).$ |
| title | Capacity and Hausdorff measure in Musielak-Orlicz-Sobolev spaces |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2503.12849 |