Hörmander's solution of the ¯ ∂ -equation with compact support
Language
en
Document de travail - Pré-publication
English Abstract
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 ...Read more >
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.Read less <
Origin
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