Constructing spaces of analytic functions through binormalizing sequences
Volume 106 / 2006
Abstract
H. Jiang and C. Lin [Chinese Ann. Math. 23 (2002)] proved that there exist infinitely many Banach spaces, called refined Besov spaces, lying strictly between the Besov spaces $B_{p,q}^s(\Bbb R^n)$ and $\bigcup_{t>s}B_{p,q}^t(\Bbb R^n)$. In this paper, we prove a similar result for the analytic Besov spaces on the unit disc $\Bbb D$. We base our construction of the intermediate spaces on operator theory, or, more specifically, the theory of symmetrically normed ideals, introduced by I. Gohberg and M. Krein. At the same time, we use these spaces as models to provide criteria for several types of operators on $H^2$, including Hankel and composition operators, to belong to certain symmetrically normed ideals generated by binormalizing sequences.
