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On the \(\bar \partial\)-problem with L 2-estimates on a Riemann surface

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Abstract

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.

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References

  1. R. C. Ganning and R. Narasimhan, “Immersion of open Riemann surfaces,” Math. Ann. 174, 103–108 (1967).

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  2. H. Hedenmalm, “On Hörmander’s solution of the ā-equation,” arXiv: 1311.2020 [math.AP].

  3. L. Hörmander, Notions of Convexity (Birkhäuser, Boston, MA, 1994), Prog. Math. 127.

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  4. T. Napier and M. Ramachandran, An Introduction to Riemann Surfaces (Springer, New York, 2011).

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Authors and Affiliations

  1. Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia

    E. M. Chirka

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  1. E. M. Chirka
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Correspondence to E. M. Chirka.

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Original Russian Text © E.M. Chirka, 2015, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2015, Vol. 290, pp. 280–292.

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Chirka, E.M. On the \(\bar \partial\)-problem with L 2-estimates on a Riemann surface. Proc. Steklov Inst. Math. 290, 264–276 (2015). https://doi.org/10.1134/S0081543815060231

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  • DOI: https://doi.org/10.1134/S0081543815060231

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