An Andreotti-grauert Theorem with L Estimates
نویسنده
چکیده
By a theorem of Andreotti and Grauert if ω is a (p, q) current, q < n, in a Stein manifold, ∂̄ closed and with compact support, then there is a solution u to ∂̄u = ω still with compact support. The main result of this work is to show that if moreover ω ∈ L(dm), where m is a suitable Lebesgue measure on the Stein manifold, then we have a solution u with compact support and in L(dm). We prove it by estimates in L spaces with weights. In a second part, we prove directly that there are global L(dm)−L(dm) solutions for the ∂̄ equation on Stein manifolds. This gives, again by duality, another proof for the main result.
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