Pointwise estimates for rough operators in a metric measure framework under some Ahlfors regularity conditions
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866910046241161216 |
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| author | Chamorro, Diego Marcoci, Anca-Nicoleta Marcoci, Liviu-Gabriel |
| author_facet | Chamorro, Diego Marcoci, Anca-Nicoleta Marcoci, Liviu-Gabriel |
| contents | We establish a new pointwise estimate for a class of rough operators in the setting of metric measure spaces endowed with a measure which is Ahlfors regular. This pointwise inequality can be divided in two steps: the first one relies in a subrepresentation formula that involves a modified Riesz potential and the upper gradient of the function considered and the second step gives a pointwise control of the Riesz potential in terms of a maximal function and a Morrey norm. We also investigate a family of functional inequalities that can be deduced from this pointwise estimate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_08186 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Pointwise estimates for rough operators in a metric measure framework under some Ahlfors regularity conditions Chamorro, Diego Marcoci, Anca-Nicoleta Marcoci, Liviu-Gabriel Functional Analysis We establish a new pointwise estimate for a class of rough operators in the setting of metric measure spaces endowed with a measure which is Ahlfors regular. This pointwise inequality can be divided in two steps: the first one relies in a subrepresentation formula that involves a modified Riesz potential and the upper gradient of the function considered and the second step gives a pointwise control of the Riesz potential in terms of a maximal function and a Morrey norm. We also investigate a family of functional inequalities that can be deduced from this pointwise estimate. |
| title | Pointwise estimates for rough operators in a metric measure framework under some Ahlfors regularity conditions |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2603.08186 |