Heisenberg Hausdorff Dimensionof Besicovitch Sets
We consider (bounded) Besicovitch sets in the Heisenberg group and prove that Lp estimates forthe Kakeya maximal function imply lower bounds for their Heisenberg Hausdorff dimension.
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| Format: | Article |
| Language: | English |
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De Gruyter
2014-01-01
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| Series: | Analysis and Geometry in Metric Spaces |
| Subjects: | |
| Online Access: | https://doi.org/10.2478/agms-2014-0013 |
| _version_ | 1818585857829896192 |
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| author | Venieri Laura |
| author_facet | Venieri Laura |
| author_sort | Venieri Laura |
| collection | DOAJ |
| description | We consider (bounded) Besicovitch sets in the Heisenberg group and prove that Lp estimates forthe Kakeya maximal function imply lower bounds for their Heisenberg Hausdorff dimension. |
| first_indexed | 2024-12-16T08:43:44Z |
| format | Article |
| id | doaj.art-01ac4a1f7ef240eb9940ae2fcf4030ec |
| institution | Directory Open Access Journal |
| issn | 2299-3274 |
| language | English |
| last_indexed | 2024-12-16T08:43:44Z |
| publishDate | 2014-01-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Analysis and Geometry in Metric Spaces |
| spelling | doaj.art-01ac4a1f7ef240eb9940ae2fcf4030ec2022-12-21T22:37:37ZengDe GruyterAnalysis and Geometry in Metric Spaces2299-32742014-01-012110.2478/agms-2014-0013agms-2014-0013Heisenberg Hausdorff Dimensionof Besicovitch SetsVenieri Laura0Department of Mathematics and Statistics, P.O. Box 68 (Gustaf Hällströmin katu 2b),FI-00014 University of Helsinki, Finland We consider (bounded) Besicovitch sets in the Heisenberg group and prove that Lp estimates forthe Kakeya maximal function imply lower bounds for their Heisenberg Hausdorff dimension.https://doi.org/10.2478/agms-2014-0013besicovitch set kakeya maximal function heisenberg group hausdorff dimension |
| spellingShingle | Venieri Laura Heisenberg Hausdorff Dimensionof Besicovitch Sets Analysis and Geometry in Metric Spaces besicovitch set kakeya maximal function heisenberg group hausdorff dimension |
| title | Heisenberg Hausdorff Dimensionof Besicovitch Sets |
| title_full | Heisenberg Hausdorff Dimensionof Besicovitch Sets |
| title_fullStr | Heisenberg Hausdorff Dimensionof Besicovitch Sets |
| title_full_unstemmed | Heisenberg Hausdorff Dimensionof Besicovitch Sets |
| title_short | Heisenberg Hausdorff Dimensionof Besicovitch Sets |
| title_sort | heisenberg hausdorff dimensionof besicovitch sets |
| topic | besicovitch set kakeya maximal function heisenberg group hausdorff dimension |
| url | https://doi.org/10.2478/agms-2014-0013 |
| work_keys_str_mv | AT venierilaura heisenberghausdorffdimensionofbesicovitchsets |