Zobrazeno 1 - 10
of 23
pro vyhledávání: '"Patrick W. Darko"'
Autor:
Patrick W. Darko, Clement H. Lutterodt
Publikováno v:
International Journal of Mathematics and Mathematical Sciences, Vol 2004, Iss 19, Pp 969-974 (2004)
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 sa
Externí odkaz:
https://doaj.org/article/32c8a2dbee4440cebce119fd15ba82fd
Autor:
Patrick W. Darko
Publikováno v:
International Journal of Mathematics and Mathematical Sciences, Vol 32, Iss 6, Pp 383-386 (2002)
Cohomology with bounds are used to globalize a result of Hörmander obtaining Carleman estimates for the Cauchy-Riemann operator on Stein manifolds.
Externí odkaz:
https://doaj.org/article/daf9e6cf8d5f435cbe149fb686e39259
Autor:
Patrick W. Darko
Publikováno v:
International Journal of Mathematics and Mathematical Sciences, Vol 29, Iss 4, Pp 187-194 (2002)
The Cauchy-Riemann equation is solved with LP-Sobolev space estimates and the result is used to obtain vanishing theorems on locally polycylindrical domains.
Externí odkaz:
https://doaj.org/article/e7f15d18b421448d8a20709874dcd6f8
Autor:
Patrick W. Darko
Publikováno v:
International Journal of Mathematics and Mathematical Sciences, Vol 30, Iss 10, Pp 621-625 (2002)
Let Ω be a relatively compact subdomain of a complex manifold, exhaustable by Stein open sets. We give a necessary and sufficient condition for Ω to be Stein, in terms of L2 -estimates for the ∂¯-operator, equivalent to the condition of Markoe (
Externí odkaz:
https://doaj.org/article/c43386c924f44fa3a5110ea65bb9933b
Autor:
Patrick W. Darko
Publikováno v:
Rendiconti di Matematica e delle Sue Applicazioni, Vol 19, Iss 3, Pp 417-426 (1999)
L^p estimates are obtained for the \partial-operator on a generalization of a polycylinder called a locally polycylindrical domain and the estimates are applied to the solution of the Corona and the Gleason problems through cohomology with bounds.
Externí odkaz:
https://doaj.org/article/07d17ea4aa82410ba622768714126bd9
Autor:
Patrick W. Darko
Publikováno v:
International Journal of Mathematics and Mathematical Sciences, Vol 30, Iss 11, Pp 705-707 (2002)
Continuous solutions with continuous data and Lp solutions with Lp data are obtained for the complex Monge-Ampère equation on bounded domains, without requiring any smoothness of the domains.
Externí odkaz:
https://doaj.org/article/dd8d33373ec84e5eb10b2ebe8b733500
Autor:
Clement H. Lutterodt, Patrick W. Darko
Publikováno v:
International Journal of Mathematics and Mathematical Sciences. 2004:969-974
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 s
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::283621057aefd84c992f358fc5f3f06a
https://doi.org/10.1155/s0161171204308197
https://doi.org/10.1155/s0161171204308197
Autor:
Patrick W. Darko
Publikováno v:
Complex Variables, Theory and Application: An International Journal. 47:929-934
Holder estimates for the ∂¯-operator are obtained on polycylinders and applied to a number of problems-cohomology with bounds, the corona problem and approximation of Holder functions by holomorphic functions.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::c106dafbd713d855ff1f8f8d59887d95
https://doi.org/10.1080/02781070290034629
https://doi.org/10.1080/02781070290034629
Autor:
Patrick W. Darko
Publikováno v:
International Journal of Mathematics and Mathematical Sciences, Vol 29, Iss 12, Pp 749-752 (2002)
It is shown that Fefferman's mapping theorem extends to the case of manifolds, that is a biholomorphic map between two strictly pseudoconvex manifolds extends smoothly to their boundaries.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a838c1ff50773ebb40f70fc246975a85
https://doaj.org/article/e99feebfe0944115a329190074c83f06
https://doaj.org/article/e99feebfe0944115a329190074c83f06
Autor:
Patrick W. Darko
Publikováno v:
Mathematical Proceedings of the Cambridge Philosophical Society. 129:73-76
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::94b55f8407ac40335b65befee21c9f3a
https://doi.org/10.1017/s0305004100004436
https://doi.org/10.1017/s0305004100004436