Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-08T06:26:27.623Z Has data issue: false hasContentIssue false
  • English
  • Français

The Ohsawa-Takegoshi Extension Theorem on Some Unbounded Sets

Published online by Cambridge University Press:  11 January 2016

Żywomir Dinew
Żywomir Dinew*
Affiliation:
Jagiellonian University, Institute of Mathematics, Reymonta 4, 30-059 Kraków, Poland, [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We use a method of Berndtsson to obtain a simplification of Ohsawa’s result concerning extension of L2-holomorphic functions. We also study versions of the Ohsawa-Takegoshi theorem for some unbounded pseudoconvex domains, with an application to the theory of Bergman spaces. Using these methods we improve some constants, that arise in related inequalities.

Keywords

32D1532A36
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 188 , December 2007 , pp. 19 - 30
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2007

References

[Be1] Berndtsson, B., The extension theorem of Ohsawa-Takegoshi and the theorem of Donnelly-Fefferman, Ann. Inst. Fourier, 46 (1996), 1083–1094.Google Scholar
[Be2] Berndtsson, B., Integral formulas and the Ohsawa-Takegoshi extension theorem, Sci. in China Ser. A, 48 (2005), 61–73.Google Scholar
[B1] Blocki, Z., Some estimates for the Bergman kernel and metric in terms of logarithmic capacity, Nagoya Math. J., to appear.Google Scholar
[D-H] Diederich, K. and Herbort, G., An alternative proof of an extension theorem of T. Ohsawa, Michigan Math. J., 46 (1999), 347–360.Google Scholar
[H] Hormander, L., An Introduction to Complex Analysis in Several Variables, North-Holland, 1989.Google Scholar
[J-P] Jarnicki, M. and Pflug, P., Invariant Distances and Metrics in Complex Analysis-Revisited, Diss. Math., 430 (2005), 1–192.Google Scholar
[O1] Ohsawa, T., On the extension of L2 holomorphic functions III: negligible weights, Math. Z., 219 (1995), 215–226.Google Scholar
[O2] Ohsawa, T., Addendum to “On the Bergman kernel of hyperconvex domains”, Nagoya Math. J., 137 (1995), 145–148.Google Scholar
[O3] Ohsawa, T., On the extension of L2 holomorphic functions V - effects of generalization, Nagoya Math. J., 161 (2001), 1–21.Google Scholar
[O-T] Ohsawa, T. and Takegoshi, K., On the extension of L 2 holomorphic functions, Math. Z., 195 (1987), 197–204.Google Scholar
[S] Suita, N., Capacities and kernels on Riemann surfaces, Arch. Ration. Mech. Anal., 46 (1972), 212–217.Google Scholar
[W] Wiegerinck, J., Domains with finite dimensional Bergman space, Math. Z., 187 (1984), 559–562.Google Scholar