Holomorphic $L^{p}$-functions on coverings of strongly pseudoconvex manifolds
HTML articles powered by AMS MathViewer
- by Alexander Brudnyi PDF
- Proc. Amer. Math. Soc. 137 (2009), 227-234 Request permission
Abstract:
In this paper we show how to construct holomorphic $L^{p}$-functions on unbranched coverings of strongly pseudoconvex manifolds. Also, we prove some extension and approximation theorems for such functions.References
- Lutz Bungart, On analytic fiber bundles. I. Holomorphic fiber bundles with infinite dimensional fibers, Topology 7 (1967), 55–68. MR 222338, DOI 10.1016/0040-9383(86)90015-7
- Alexander Brudnyi, On holomorphic $L^2$ functions on coverings of strongly pseudoconvex manifolds, Publ. Res. Inst. Math. Sci. 43 (2007), no. 4, 963–976. MR 2389789
- Alexander Brudnyi, Hartogs type theorems for $\textrm {CR}\ L^2$ functions on coverings of strongly pseudoconvex manifolds, Nagoya Math. J. 189 (2008), 27–47. MR 2396582, DOI 10.1017/S0027763000009491
- Alexander Brudnyi, On holomorphic functions of slow growth on coverings of strongly pseudoconvex manifolds, J. Funct. Anal. 249 (2007), no. 2, 354–371. MR 2345336, DOI 10.1016/j.jfa.2007.03.020
- Alexander Brudnyi, Representation of holomorphic functions on coverings of pseudoconvex domains in Stein manifolds via integral formulas on these domains, J. Funct. Anal. 231 (2006), no. 2, 418–437. MR 2195338, DOI 10.1016/j.jfa.2005.06.004
- Henri Cartan, Sur les fonctions de plusieurs variables complexes: les espaces analytiques, Proc. Internat. Congress Math. 1958., Cambridge Univ. Press, New York, 1960, pp. 33–52 (French). MR 0117763
- M. Gromov, G. Henkin, and M. Shubin, Holomorphic $L^2$ functions on coverings of pseudoconvex manifolds, Geom. Funct. Anal. 8 (1998), no. 3, 552–585. MR 1631263, DOI 10.1007/s000390050066
- Yu. Laĭterer, Holomorphic vector bundles and the Oka-Grauert principle, Current problems in mathematics. Fundamental directions, Vol. 10 (Russian), Itogi Nauki i Tekhniki, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1986, pp. 75–121, 283 (Russian). Translated by D. N. Akhiezer. MR 894263
- Reinhold Remmert, Sur les espaces analytiques holomorphiquement séparables et holomorphiquement convexes, C. R. Acad. Sci. Paris 243 (1956), 118–121 (French). MR 79808
- Walter Rudin, Real and complex analysis, 2nd ed., McGraw-Hill Series in Higher Mathematics, McGraw-Hill Book Co., New York-Düsseldorf-Johannesburg, 1974. MR 0344043
Additional Information
- Alexander Brudnyi
- Affiliation: Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta T2N 1N4, Canada
- MR Author ID: 292684
- Email: albru@math.ucalgary.ca
- Received by editor(s): December 28, 2007
- Published electronically: August 13, 2008
- Additional Notes: This research was supported in part by NSERC
- Communicated by: Mikhail Shubin
- © Copyright 2008 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 137 (2009), 227-234
- MSC (2000): Primary 32T15; Secondary 32L05, 46E15
- DOI: https://doi.org/10.1090/S0002-9939-08-09563-4
- MathSciNet review: 2439445