International Journal of Mathematics and Mathematical Sciences
Volume 25 (2001), Issue 1, Pages 19-31
doi:10.1155/S0161171201001971

Finite-rank intermediate Hankel operators on the Bergman space

Takahiko Nakazi1 and Tomoko Osawa2

1Department of Mathematics, Hokkaido University, Sapporo 060, Japan
2Mathematical and Scientific Subjects, Asahikawa National College of Technology, Asahikawa 071, Japan

Received 11 January 1998

Copyright © 2001 Takahiko Nakazi and Tomoko Osawa. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.