Cohomology with Lp-bounds on polycylinders
Let Ω=Ω1×…×Ωn be a polycylinder in ℂn, that is each Ωj is bounded, non-empty and open in ℂ. The main result proved here is that, if Bp is the sheaf of germs of Lp-holomorphic functions on Ω¯ then Hq(Ω¯,Bp)=0 for q≥1. The proof of this is then used to establish a Leray's Isomorphism with Lp-boun...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
1995-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171295000603 |
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| _version_ | 1832558106806059008 |
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| author | P. W. Darko C. H. Lutterodt |
| author_facet | P. W. Darko C. H. Lutterodt |
| author_sort | P. W. Darko |
| collection | DOAJ |
| description | Let Ω=Ω1×…×Ωn be a polycylinder in ℂn, that is each Ωj is bounded,
non-empty and open in ℂ. The main result proved here is that, if Bp is the sheaf of germs of
Lp-holomorphic functions on Ω¯ then Hq(Ω¯,Bp)=0 for q≥1. The proof of this is then used to
establish a Leray's Isomorphism with Lp-bounds theorem. |
| format | Article |
| id | doaj-art-7761a6f35f974b36839e59691ee0e19c |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1995-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-7761a6f35f974b36839e59691ee0e19c2025-02-03T01:33:15ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251995-01-0118347548410.1155/S0161171295000603Cohomology with Lp-bounds on polycylindersP. W. Darko0C. H. Lutterodt1Department of Mathematics, Howard University, Washington, D.C. 20059, USADepartment of Mathematics, Howard University, Washington, D.C. 20059, USALet Ω=Ω1×…×Ωn be a polycylinder in ℂn, that is each Ωj is bounded, non-empty and open in ℂ. The main result proved here is that, if Bp is the sheaf of germs of Lp-holomorphic functions on Ω¯ then Hq(Ω¯,Bp)=0 for q≥1. The proof of this is then used to establish a Leray's Isomorphism with Lp-bounds theorem.http://dx.doi.org/10.1155/S0161171295000603sheaf cohomology-Lp bounds∂¯-equation. |
| spellingShingle | P. W. Darko C. H. Lutterodt Cohomology with Lp-bounds on polycylinders International Journal of Mathematics and Mathematical Sciences sheaf cohomology-Lp bounds ∂¯-equation. |
| title | Cohomology with Lp-bounds on polycylinders |
| title_full | Cohomology with Lp-bounds on polycylinders |
| title_fullStr | Cohomology with Lp-bounds on polycylinders |
| title_full_unstemmed | Cohomology with Lp-bounds on polycylinders |
| title_short | Cohomology with Lp-bounds on polycylinders |
| title_sort | cohomology with lp bounds on polycylinders |
| topic | sheaf cohomology-Lp bounds ∂¯-equation. |
| url | http://dx.doi.org/10.1155/S0161171295000603 |
| work_keys_str_mv | AT pwdarko cohomologywithlpboundsonpolycylinders AT chlutterodt cohomologywithlpboundsonpolycylinders |