On a proposed characterization of Schatten-class composition operators
Authors:
Jingbo Xia
Affiliation:
Department of Mathematics, State University of New York at Buffalo, Buffalo, New York 14260
Abstract:
For an analytic function which maps the open unit disc to itself, let be the operator of composition with on the Bergman space . It has been a longstanding problem to determine whether or not the membership of in the Schatten class , , is equivalent to the condition that the function has a finite integral with respect to the Möbius-invariant measure on . We show that the answer is negative when .