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Hörmander's solution of the ¯ ∂ -equation with compact support
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | AMAR, Eric | |
| dc.date.accessioned | 2024-04-04T03:14:56Z | |
| dc.date.available | 2024-04-04T03:14:56Z | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/194109 | |
| dc.description.abstractEn | This work is a complement of the study on Hörmander's solution of the ¯ ∂ equation initialised by H. Hedenmalm. Let ϕ be a strictly plurisubharmonic function of class C 2 in C n ; let c ϕ (z) be the smallest eigenvalue of i∂ ¯ ∂ϕ then ∀z ∈ C n , c ϕ (z) > 0. We denote by L 2 p,q (C n , e ϕ) the (p, q) currents with coefficients in L 2 (C n , e ϕ). We prove that if ω ∈ L 2 p,q (C n , e ϕ), ¯ ∂ω = 0 for q < n then there is a solution u ∈ L 2 p,q−1 (C n , c ϕ e ϕ) of ¯ ∂u = ω. This is done via a theorem giving a solution with compact support if the data has compact support. | |
| dc.language.iso | en | |
| dc.title.en | Hörmander's solution of the ¯ ∂ -equation with compact support | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math]/Variables complexes [math.CV] | |
| dc.identifier.arxiv | 1604.04744 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-01301669 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01301669v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=AMAR,%20Eric&rft.genre=preprint |
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