On Hausdorff content maximal operator and Riesz potential for non-measurable functions
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911882264182784 |
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| author | Harjulehto, Petteri Hurri-Syrjänen, Ritva |
| author_facet | Harjulehto, Petteri Hurri-Syrjänen, Ritva |
| contents | We introduce Riesz potentials for non-Lebesgue measurable functions by taking the integrals in the sense of Choquet with respect to Hausdorff content and prove boundedness results for these operators. Some earlier results are recovered or extended now using integrals taken in the sense of Choquet with respect to Hausdorff content. Some earlier results also for maximal operators are considered, but now for non-measurable functions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_12113 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Hausdorff content maximal operator and Riesz potential for non-measurable functions Harjulehto, Petteri Hurri-Syrjänen, Ritva Functional Analysis 42B25 (28A25, 28A20) We introduce Riesz potentials for non-Lebesgue measurable functions by taking the integrals in the sense of Choquet with respect to Hausdorff content and prove boundedness results for these operators. Some earlier results are recovered or extended now using integrals taken in the sense of Choquet with respect to Hausdorff content. Some earlier results also for maximal operators are considered, but now for non-measurable functions. |
| title | On Hausdorff content maximal operator and Riesz potential for non-measurable functions |
| topic | Functional Analysis 42B25 (28A25, 28A20) |
| url | https://arxiv.org/abs/2405.12113 |