Geodesic
On the $\bar \partial $-problem with $L^2$-estimates on a Riemann surface
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems of mathematics, mechanics, and mathematical physics, Tome 290 (2015), pp. 280-292

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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. 
@article{TM_2015_290_a22,
     author = {E. M. Chirka},
     title = {On the $\bar \partial $-problem with $L^2$-estimates on a {Riemann} surface},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {280--292},
     publisher = {mathdoc},
     volume = {290},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2015_290_a22/}
}
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E. M. Chirka. On the $\bar \partial $-problem with $L^2$-estimates on a Riemann surface. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems of mathematics, mechanics, and mathematical physics, Tome 290 (2015), pp. 280-292. http://geodesic.mathdoc.fr/item/TM_2015_290_a22/