Sobolev space estimates for solutions of the equation ∂¯u=f on polycylinders
In trying to improve Weinstock's results on approximation by holomorphic functions on certain product domains, we are led to estimates in Sobolev spaces for the ∂¯-operator on polycylinders for (γ,q)-forms. This generalizes our results for the same operator on polycylinders previously obtained,...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2004-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171204308197 |
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| _version_ | 1850156927125815296 |
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| author | Patrick W. Darko Clement H. Lutterodt |
| author_facet | Patrick W. Darko Clement H. Lutterodt |
| author_sort | Patrick W. Darko |
| collection | DOAJ |
| description | In trying to improve Weinstock's results on approximation
by holomorphic functions on certain product domains, we
are led to estimates in Sobolev spaces for the ∂¯-operator on polycylinders for (γ,q)-forms.
This generalizes our results for the same operator on
polycylinders previously obtained, and can be applied to a number
of other problems such as the Corona problem. |
| format | Article |
| id | doaj-art-32c8a2dbee4440cebce119fd15ba82fd |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2004-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-32c8a2dbee4440cebce119fd15ba82fd2025-08-20T02:24:19ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252004-01-0120041996997410.1155/S0161171204308197Sobolev space estimates for solutions of the equation ∂¯u=f on polycylindersPatrick W. Darko0Clement H. Lutterodt1Department of Mathematics and Computer Science, Lincoln University, 19352, PA, USADepartment of Mathematics, Howard University, Washington, DC 20059, USAIn trying to improve Weinstock's results on approximation by holomorphic functions on certain product domains, we are led to estimates in Sobolev spaces for the ∂¯-operator on polycylinders for (γ,q)-forms. This generalizes our results for the same operator on polycylinders previously obtained, and can be applied to a number of other problems such as the Corona problem.http://dx.doi.org/10.1155/S0161171204308197 |
| spellingShingle | Patrick W. Darko Clement H. Lutterodt Sobolev space estimates for solutions of the equation ∂¯u=f on polycylinders International Journal of Mathematics and Mathematical Sciences |
| title | Sobolev space estimates for solutions of the equation
∂¯u=f on polycylinders |
| title_full | Sobolev space estimates for solutions of the equation
∂¯u=f on polycylinders |
| title_fullStr | Sobolev space estimates for solutions of the equation
∂¯u=f on polycylinders |
| title_full_unstemmed | Sobolev space estimates for solutions of the equation
∂¯u=f on polycylinders |
| title_short | Sobolev space estimates for solutions of the equation
∂¯u=f on polycylinders |
| title_sort | sobolev space estimates for solutions of the equation ∂¯u f on polycylinders |
| url | http://dx.doi.org/10.1155/S0161171204308197 |
| work_keys_str_mv | AT patrickwdarko sobolevspaceestimatesforsolutionsoftheequationufonpolycylinders AT clementhlutterodt sobolevspaceestimatesforsolutionsoftheequationufonpolycylinders |