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Journal of Function Spaces
Volume 2015 (2015), Article ID 295759, 10 pages
http://dx.doi.org/10.1155/2015/295759
Research Article

Gain of Regularity in Extension Problem on Convex Domains

Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Ulica Umultowska 87, 61-614 Poznan, Poland

Received 19 March 2015; Accepted 18 June 2015

Academic Editor: Alberto Fiorenza

Copyright © 2015 M. Jasiczak. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We investigate the extension problem from higher codimensional linear subvarieties on convex domains of finite type. We prove that there exists a constant such that on Bergman spaces with there appears the so-called “gain regularity.” The constant depends on the minimum of the dimension and the codimension of the subvariety. This means that the space of functions which admit an extension to a function in the Bergman space is strictly larger than , where is a subvariety.