论文标题
Banach值$ \ bar \ bar \ partial $问题的$ l^\ infty $估计
$L^\infty$ Estimates for the Banach-valued $\bar\partial$ problem in a Disk
论文作者
论文摘要
我们研究了微分方程$ \ frac {\ partial g} {\ partial \ bar z} = g $，带有无界的banach-valued bochner bochner可测量的函数$ g $ in Open单位磁盘$ \ mathbb d \ subset \ subset \ subset \ mathbb c $。我们证明，在某些条件下，关于$ g $的增长和基本支持，这种方程式具有连续线性操作员给出的有限解决方案。所获得的结果适用于在复杂的Unsutative Unital Banach代数中的$ \ Mathbb d $上的有界全态函数代数的BANACH价值电晕问题。
We study the differential equation $\frac{\partial G}{\partial\bar z}=g$ with an unbounded Banach-valued Bochner measurable function $g$ on the open unit disk $\mathbb D\subset\mathbb C$. We prove that under some conditions on the growth and essential support of $g$ such equation has a bounded solution given by a continuous linear operator. The obtained results are applicable to the Banach-valued corona problem for the algebra of bounded holomorphic functions on $\mathbb D$ with values in a complex commutative unital Banach algebra.
