Outer functions in Qp#, Qp,0#
For 0<p<∞, Qp# (Qp,0#) is the class of meromorphic functions f defined in the unit disk D={z:|z|<1} satisfying supw∈D∬D(f#(z))2gp(z,w)dσz<∞ (limw→∂D∬D(f#(z))2gp(z,w)dσz=0), where g(z,w) is Green's function of D. Criteria for funtions f to belong to Qp# (Qp,0#) are given by the...
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| Format: | Article |
| Language: | English |
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Wiley
2004-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2004/493269 |
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| _version_ | 1850232890986594304 |
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| author | Rauno Aulaskari Hasi Wulan |
| author_facet | Rauno Aulaskari Hasi Wulan |
| author_sort | Rauno Aulaskari |
| collection | DOAJ |
| description | For 0<p<∞, Qp# (Qp,0#) is the class of meromorphic functions f defined in the unit disk D={z:|z|<1} satisfying supw∈D∬D(f#(z))2gp(z,w)dσz<∞ (limw→∂D∬D(f#(z))2gp(z,w)dσz=0), where g(z,w) is Green's function of D. Criteria for funtions f to belong to Qp# (Qp,0#) are given by the Ahlfors-Shimizu characteristic. Further, outer functions in Qp# (Qp,0#) are characterized and shown that every function in Qp# (Qp,0#) can be represented as the quotient of two functions in H∞∩Qp# (H∞∩Qp,0#). |
| format | Article |
| id | doaj-art-0d042553616a45839b40870ea9dda10d |
| institution | OA Journals |
| issn | 0972-6802 |
| language | English |
| publishDate | 2004-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-0d042553616a45839b40870ea9dda10d2025-08-20T02:03:04ZengWileyJournal of Function Spaces and Applications0972-68022004-01-0121172410.1155/2004/493269Outer functions in Qp#, Qp,0#Rauno Aulaskari0Hasi Wulan1Department of Mathematics, University of Joensuu, P.O. Box 111, FIN-80101 Joensuu, FinlandDepartment of Mathematics, University of Joensuu, P.O. Box 111, FIN-80101 Joensuu, FinlandFor 0<p<∞, Qp# (Qp,0#) is the class of meromorphic functions f defined in the unit disk D={z:|z|<1} satisfying supw∈D∬D(f#(z))2gp(z,w)dσz<∞ (limw→∂D∬D(f#(z))2gp(z,w)dσz=0), where g(z,w) is Green's function of D. Criteria for funtions f to belong to Qp# (Qp,0#) are given by the Ahlfors-Shimizu characteristic. Further, outer functions in Qp# (Qp,0#) are characterized and shown that every function in Qp# (Qp,0#) can be represented as the quotient of two functions in H∞∩Qp# (H∞∩Qp,0#).http://dx.doi.org/10.1155/2004/493269 |
| spellingShingle | Rauno Aulaskari Hasi Wulan Outer functions in Qp#, Qp,0# Journal of Function Spaces and Applications |
| title | Outer functions in Qp#, Qp,0# |
| title_full | Outer functions in Qp#, Qp,0# |
| title_fullStr | Outer functions in Qp#, Qp,0# |
| title_full_unstemmed | Outer functions in Qp#, Qp,0# |
| title_short | Outer functions in Qp#, Qp,0# |
| title_sort | outer functions in qp qp 0 |
| url | http://dx.doi.org/10.1155/2004/493269 |
| work_keys_str_mv | AT raunoaulaskari outerfunctionsinqpqp0 AT hasiwulan outerfunctionsinqpqp0 |