论文标题
$ l^2 $估计$ \ mathbb {c}^n $ in convex域上的poincaré-lelong方程式的估计值
$L^2$ estimates of Poincaré-Lelong equations on convex domains in $\mathbb{C}^n$
论文作者
论文摘要
在本文中，我们证明了Poincaré-Lelong方程的解决方案$ \ sqrt {-1} \ partial \ bar {\ partial} u = f $在严格凸的域$ \ subset \ subset \ subset \ subset \ subset \ subset \ subset \ subset \ subset \ mathb {c} c}^n $ $ geq $ f $ f $ f $ f $ f $中并在加权希尔伯特空间中$ l^2 _ {（1,1）}（ω，e^{ - φ}）$。本文的新颖性是将加权的$ l^2 $版本的PoincaréLemma用于真正的$ 2 $ -FORMS，然后将Hörmander的$ L^2 $ Solutions应用于Cauchy-Riemann方程。
In this paper, we prove the existence of solutions of the Poincaré-Lelong equation $\sqrt{-1}\partial\bar{\partial}u=f$ on a strictly convex bounded domain $Ω\subset\mathbb{C}^n$ $(n\geq1)$, where $f$ is a $d$-closed $(1,1)$ form and is in the weighted Hilbert space $L^2_{(1,1)}(Ω,e^{-φ})$. The novelty of this paper is to apply a weighted $L^2$ version of Poincaré Lemma for real $2$-forms, and then apply Hörmander's $L^2$ solutions for Cauchy-Riemann equations.
