Constructing spaces of analytic functions through binormalizing sequences

Mark C. Ho; Mu Ming Wong

Colloquium Mathematicae (2006)

  • Volume: 106, Issue: 2, page 177-195
  • ISSN: 0010-1354

Abstract

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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 ( ) and t > s B p , q t ( ) . 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.

How to cite

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Mark C. Ho, and Mu Ming Wong. "Constructing spaces of analytic functions through binormalizing sequences." Colloquium Mathematicae 106.2 (2006): 177-195. <http://eudml.org/doc/283892>.

@article{MarkC2006,
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 $B_\{p,q\}^s(ℝⁿ)$ and $⋃_\{t>s\}B_\{p,q\}^t(ℝⁿ)$. 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.},
author = {Mark C. Ho, Mu Ming Wong},
journal = {Colloquium Mathematicae},
keywords = {Besov spaces; symmetrical normed ideals; binormalizing sequences; Hankel operators; Berezin transform},
language = {eng},
number = {2},
pages = {177-195},
title = {Constructing spaces of analytic functions through binormalizing sequences},
url = {http://eudml.org/doc/283892},
volume = {106},
year = {2006},
}

TY - JOUR
AU - Mark C. Ho
AU - Mu Ming Wong
TI - Constructing spaces of analytic functions through binormalizing sequences
JO - Colloquium Mathematicae
PY - 2006
VL - 106
IS - 2
SP - 177
EP - 195
AB - 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 $B_{p,q}^s(ℝⁿ)$ and $⋃_{t>s}B_{p,q}^t(ℝⁿ)$. 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.
LA - eng
KW - Besov spaces; symmetrical normed ideals; binormalizing sequences; Hankel operators; Berezin transform
UR - http://eudml.org/doc/283892
ER -

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