Geodesic
On the $\bar \partial $-problem with $L^2$-estimates on a Riemann surface
Informatics and Automation, Modern problems of mathematics, mechanics, and mathematical physics, Tome 290 (2015), pp. 280-292 
E. M. Chirka. On the $\bar \partial $-problem with $L^2$-estimates on a Riemann surface. Informatics and Automation, Modern problems of mathematics, mechanics, and mathematical physics, Tome 290 (2015), pp. 280-292. http://geodesic.mathdoc.fr/item/TRSPY_2015_290_a22/
@article{TRSPY_2015_290_a22,
     author = {E. M. Chirka},
     title = {On the $\bar \partial $-problem with $L^2$-estimates on a {Riemann} surface},
     journal = {Informatics and Automation},
     pages = {280--292},
     year = {2015},
     volume = {290},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2015_290_a22/}
}
TY  - JOUR
AU  - E. M. Chirka
TI  - On the $\bar \partial $-problem with $L^2$-estimates on a Riemann surface
JO  - Informatics and Automation
PY  - 2015
SP  - 280
EP  - 292
VL  - 290
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2015_290_a22/
LA  - ru
ID  - TRSPY_2015_290_a22
ER  - 
%0 Journal Article
%A E. M. Chirka
%T On the $\bar \partial $-problem with $L^2$-estimates on a Riemann surface
%J Informatics and Automation
%D 2015
%P 280-292
%V 290
%U http://geodesic.mathdoc.fr/item/TRSPY_2015_290_a22/
%G ru
%F TRSPY_2015_290_a22

Voir la notice de l'article provenant de la source Math-Net.Ru

The $L^2$-estimates obtained by Hörmander for the solutions to the $\bar \partial $-problem are specified and complemented in the simplest one-dimensional case of Riemann surfaces.

[1] Ganning R.C., Narasimhan R., “Immersion of open Riemann surfaces”, Math. Ann., 174 (1967), 103–108 | DOI | MR

[2] Hedenmalm H., On Hörmander's solution of the $\bar \partial $-equation, E-print, 2013, arXiv: 1311.2020 [math.AP]

[3] Hörmander L., Notions of convexity, Prog. Math., 127, Birkhäuser, Boston, MA, 1994 | MR | Zbl

[4] Napier T., Ramachandran M., An introduction to Riemann surfaces, Springer, New York, 2011 | MR | Zbl