Archives

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