Gain of Regularity in Extension Problem on Convex Domains
We investigate the extension problem from higher codimensional linear subvarieties on convex domains of finite type. We prove that there exists a constant d such that on Bergman spaces Hp(D) with 1≤p<d there appears the so-called “gain regularity.” The constant d depends on the minimum of the dim...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2015-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2015/295759 |
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| Summary: | We investigate the extension problem from higher codimensional linear subvarieties on convex domains of finite type. We prove that there exists a constant d such that on Bergman spaces Hp(D) with 1≤p<d there appears the so-called “gain regularity.” The constant d 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 Hp(D) is strictly larger than Hp(D∩A), where A is a subvariety. |
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| ISSN: | 2314-8896 2314-8888 |