Q_K-spaces
by
Matts Essén
Department of Mathematics, Uppsala University, S-75106 Uppsala, Sweden

Starting from a nondecreasing function K:[0, \infty) --> [0, \infty), we introduce a Möbius-invariant Banach space Q_K of functions analytic in the unit disk in the plane where the norm is defined by

||f||QK2 = sup a in \Delta  ó õ ó õ \Delta  |f'(z)|2K(g(z, a)dA(z).

We give a general theory of these spaces which for special choices of K give most basic propertiese of Q_p-spaces. Furthermore, we have found necessary and sufficient conditions on K such that Q_K is the Bloch space or the Dirichlet space.

Date received: August 6, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cahz-31.