Abstract
We prove a necessary condition for functions which are holomorphic on a non-singular subvariety of a smoothly bounded domain of finite type in \({\mathbb{C}^{2}}\) to admit an extension to a function belonging to the Bergman space on the whole domain. The method can also be used to obtain the embedding results for the scale of Bergman spaces.
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The author was supported in years 2007–2010 by The Ministry of Science and Higher Education, Poland, grant no. N N 201 2740 33 and in 2008 by the Foundation for Polish Science. The Author was supported in years 2008–2009 by the Foundation for Polish Science.
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Jasiczak, M. Restriction of holomorphic functions on finite type domains in \({\mathbb{C}^{2}}\) . manuscripta math. 133, 1–18 (2010). https://doi.org/10.1007/s00229-010-0358-0
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DOI: https://doi.org/10.1007/s00229-010-0358-0