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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |