Constructing spaces of analytic functions through binormalizing sequences

Mark C. Ho¹ ; Mu Ming Wong²

¹ Department of Applied Mathematics National Sun Yat-Sen University Kaohsiung, Taiwan
² Department of Information Technology Meiho Institute of Technology Pington, Taiwan

Colloquium Mathematicum, Tome 106 (2006) no. 2, pp. 177-195

Résumé

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.

Détail

DOI : 10.4064/cm106-2-2

Keywords: jiang lin chinese ann math proved there exist infinitely many banach spaces called refined besov spaces lying strictly between besov spaces bbb bigcup bbb paper prove similar result analytic besov spaces unit disc bbb base construction intermediate spaces operator theory specifically theory symmetrically normed ideals introduced gohberg krein time these spaces models provide criteria several types operators including hankel composition operators belong certain symmetrically normed ideals generated binormalizing sequences