Abstract:We find integrability conditions on the initial data $f$ for the existence of solutions of the Heat problem on the Heisenberg group. From this result we characterize the weighted Lebesgue spaces for which the solutions exists a.e. when the time goes to zero. Finally we also obtain boundedness of the local maximal function associated to the heat kernel with weights.
| Subjects: | Analysis of PDEs (math.AP) |
| Cite as: | arXiv:2309.08785 [math.AP] |
| (or arXiv:2309.08785v3 [math.AP] for this version) | |
| https://doi.org/10.48550/arXiv.2309.08785 arXiv-issued DOI via DataCite |
From: Isolda Cardoso [view email]
[v1]
Fri, 15 Sep 2023 22:06:55 UTC (16 KB)
[v2]
Wed, 11 Dec 2024 15:23:28 UTC (16 KB)
[v3]
Fri, 22 May 2026 13:12:59 UTC (16 KB)
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