Lacunary elliptic maximal operator on the Heisenberg group
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916574959501312 |
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| author | Kim, Joonil Oh, Jeongtae |
| author_facet | Kim, Joonil Oh, Jeongtae |
| contents | In this paper, we prove \( L^p \) boundedness results for lacunary elliptic maximal operators on the Heisenberg group. Furthermore, we extend these \( L^p \) estimates from skew-symmetric matrices, which naturally arise in Heisenberg group operations, to arbitrary matrices \( A \), investigating how the curvature induced by \( A \) governs the \( L^p \) boundedness of lacunary circular and elliptic maximal operators. Specifically, we provide necessary and sufficient conditions on \( A \) that determine whether these operators are bounded or unbounded on \( L^p \). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_11928 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lacunary elliptic maximal operator on the Heisenberg group Kim, Joonil Oh, Jeongtae Classical Analysis and ODEs In this paper, we prove \( L^p \) boundedness results for lacunary elliptic maximal operators on the Heisenberg group. Furthermore, we extend these \( L^p \) estimates from skew-symmetric matrices, which naturally arise in Heisenberg group operations, to arbitrary matrices \( A \), investigating how the curvature induced by \( A \) governs the \( L^p \) boundedness of lacunary circular and elliptic maximal operators. Specifically, we provide necessary and sufficient conditions on \( A \) that determine whether these operators are bounded or unbounded on \( L^p \). |
| title | Lacunary elliptic maximal operator on the Heisenberg group |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2501.11928 |