Finite-rank intermediate Hankel operators on the Bergman space
Let L2=L2(D,r dr dθ/π) be the Lebesgue space on the open unit disc and let La2=L2∩ℋol(D) be the Bergman space. Let P be the orthogonal projection of L2 onto La2 and let Q be the orthogonal projection onto L¯a,02={g∈L2;g¯∈La2, g(0)=0}. Then I−P≥Q. The big Hankel operator and the small Hankel opera...
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| Format: | Article |
| Language: | English |
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Wiley
2001-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171201001971 |
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| author | Takahiko Nakazi Tomoko Osawa |
| author_facet | Takahiko Nakazi Tomoko Osawa |
| author_sort | Takahiko Nakazi |
| collection | DOAJ |
| description | Let L2=L2(D,r dr dθ/π) be the Lebesgue space on the
open unit disc and let La2=L2∩ℋol(D)
be the Bergman
space. Let P be the orthogonal projection of L2 onto La2 and let Q be the orthogonal projection onto L¯a,02={g∈L2;g¯∈La2, g(0)=0}. Then I−P≥Q. The big Hankel operator and the small
Hankel operator on La2 are defined as: for ϕ in L∞, Hϕbig(f)=(I−P)(ϕf) and Hϕsmall(f)=Q(ϕf)(f∈La2). In this paper, the finite-rank intermediate
Hankel operators between Hϕbig and Hϕsmall are studied. We are working on the
more general space, that is, the weighted Bergman space. |
| format | Article |
| id | doaj-art-8c6895d83f494abaa6d639af148edbd3 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2001-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-8c6895d83f494abaa6d639af148edbd32025-02-03T01:29:00ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252001-01-01251193110.1155/S0161171201001971Finite-rank intermediate Hankel operators on the Bergman spaceTakahiko Nakazi0Tomoko Osawa1Department of Mathematics, Hokkaido University, Sapporo 060, JapanMathematical and Scienti?c Subjects, Asahikawa National College of Technology, Asahikawa 071, JapanLet L2=L2(D,r dr dθ/π) be the Lebesgue space on the open unit disc and let La2=L2∩ℋol(D) be the Bergman space. Let P be the orthogonal projection of L2 onto La2 and let Q be the orthogonal projection onto L¯a,02={g∈L2;g¯∈La2, g(0)=0}. Then I−P≥Q. The big Hankel operator and the small Hankel operator on La2 are defined as: for ϕ in L∞, Hϕbig(f)=(I−P)(ϕf) and Hϕsmall(f)=Q(ϕf)(f∈La2). In this paper, the finite-rank intermediate Hankel operators between Hϕbig and Hϕsmall are studied. We are working on the more general space, that is, the weighted Bergman space.http://dx.doi.org/10.1155/S0161171201001971 |
| spellingShingle | Takahiko Nakazi Tomoko Osawa Finite-rank intermediate Hankel operators on the Bergman space International Journal of Mathematics and Mathematical Sciences |
| title | Finite-rank intermediate Hankel operators on the Bergman space |
| title_full | Finite-rank intermediate Hankel operators on the Bergman space |
| title_fullStr | Finite-rank intermediate Hankel operators on the Bergman space |
| title_full_unstemmed | Finite-rank intermediate Hankel operators on the Bergman space |
| title_short | Finite-rank intermediate Hankel operators on the Bergman space |
| title_sort | finite rank intermediate hankel operators on the bergman space |
| url | http://dx.doi.org/10.1155/S0161171201001971 |
| work_keys_str_mv | AT takahikonakazi finiterankintermediatehankeloperatorsonthebergmanspace AT tomokoosawa finiterankintermediatehankeloperatorsonthebergmanspace |