Subelliptic and Maximal $L^p$ Estimates for the Complex Green Operator on non-pseudoconvex domains
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912328725823488 |
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| author | Coacalle, Joel |
| author_facet | Coacalle, Joel |
| contents | We prove subelliptic estimates for ethe complex Green operator $ K_q $ at a specific level $ q $ of the $ \bar\partial_b $-complex, defined on a not necessarily pseudoconvex CR manifold satisfying the commutator finite type condition. Additionally, we obtain maximal $ L^p $ estimates for $ K_q $ by considering closed-range estimates. Our results apply to a family of manifolds that includes a class of weak $ Y(q) $ manifolds satisfying the condition $ D(q) $. We employ a microlocal decomposition and Calderón-Zygmund theory to obtain subelliptic and maximal-$ L^p $ estimates, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_10614 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Subelliptic and Maximal $L^p$ Estimates for the Complex Green Operator on non-pseudoconvex domains Coacalle, Joel Complex Variables Primary: 32W10, Secondary: 32F17, 32V35, 35A27, 35B65 We prove subelliptic estimates for ethe complex Green operator $ K_q $ at a specific level $ q $ of the $ \bar\partial_b $-complex, defined on a not necessarily pseudoconvex CR manifold satisfying the commutator finite type condition. Additionally, we obtain maximal $ L^p $ estimates for $ K_q $ by considering closed-range estimates. Our results apply to a family of manifolds that includes a class of weak $ Y(q) $ manifolds satisfying the condition $ D(q) $. We employ a microlocal decomposition and Calderón-Zygmund theory to obtain subelliptic and maximal-$ L^p $ estimates, respectively. |
| title | Subelliptic and Maximal $L^p$ Estimates for the Complex Green Operator on non-pseudoconvex domains |
| topic | Complex Variables Primary: 32W10, Secondary: 32F17, 32V35, 35A27, 35B65 |
| url | https://arxiv.org/abs/2504.10614 |