Closed Range Property for $\overline\partial$ on the Poinc$\acute{a}$re Disk
by
Xiaoshan Li
Vol. 11 No. 3 (2016) P.571~P.578
DOI: | https://doi.org/110.21915/BIMAS.2016303 |
| 10.21915/BIMAS.2016303 |
ABSTRACT
Making use of the Poinc$\acute{a}$re inequality with respect to a complete metric on the real line, we will give an elementary proof of the closed range property for $\overline\partial$-operator on the unit disk endowed with Poinc$\acute{a}$re metric.
KEYWORDS
$\overline\partial$-operator, closed range, poinc$\acute{a}$re disk.
MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 32W05, 35N15, 58J32.
MILESTONES
Received: 2016-07-23
Revised : 2016-08-16
Accepted: 2016-08-05
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