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 and . In this paper, we prove a similar result for the analytic Besov spaces on the unit disc . 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 H², including Hankel and composition operators, to belong to certain symmetrically normed ideals generated by binormalizing sequences.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm106-2-2,
author = {Mark C. Ho and Mu Ming Wong},
title = {Constructing spaces of analytic functions through binormalizing sequences},
journal = {Colloquium Mathematicae},
volume = {106},
year = {2006},
pages = {177-195},
zbl = {1110.30023},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm106-2-2}
}
Mark C. Ho; Mu Ming Wong. Constructing spaces of analytic functions through binormalizing sequences. Colloquium Mathematicae, Tome 106 (2006) pp. 177-195. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm106-2-2/