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Journal of the London Mathematical Society 1991 s2-43(3):485-508; doi:10.1112/jlms/s2-43.3.485
© 1991 by London Mathematical Society
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© Oxford University Press

Membership of Hankel Operators on the Ball in Unitary Ideals

Jonathan Arazy, Stephen D. Fisher, Svante Janson and Jaak Peetre

Department of Mathematics, University of Haifa Haifa 31999, Israel
Department of Mathematics, Northwestern University Evanston, Illinois 60208, USA
Department of Mathematics, Uppsala University Thunbergsvägen 3, S-752 38 Uppsala, Sweden
Department of Mathematics, University of Stockholm Box 6701, S-113 85 Stockholm, Sweden

We consider Hankel operators on (weighted) Bergman spaces on the unit ball in several complex variables. The main result is several, equivalent, necessary and sufficient conditions for a Hankel operator with analytic symbol to belong to the Schatten-von Neumann ideal Sp.

There is one important difference between our results, and the corresponding results in one variable; if the number of dimensions N is 2 or more, there exist non-trivial Hankel operators with analytic symbols in Sp when p > 2N, but if N = 1, the condition is p > 1.

One ingredient in the proof is an improvement of Russo's condition for integral operators on L2 to belong to Sp.


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