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Preduals of $Q_p$-spaces. II: Carleson imbeddings and atomic decompositions

Aleman, Alexandru LU ; Carlsson, Marcus LU and Persson, Anna-Maria LU (2007) In Complex Variables and Elliptic Equations 52(7). p.629-653
Abstract
Summary: In [Aleman, A., Carlsson, M. and Persson A., Preduals of $Q_p$-spaces. Complex Variables (To appear).], we have obtained a representation of the Cauchy-predual of the space $Q_p$ on the unit disc as a weak product of weighted Dirichlet and Bergman spaces. The present article is a continuation of Aleman et al. and contains several applications and further developments of those results. We investigate the relation between $Q_p$ and Carleson inequalities for functions in weighted Dirichlet spaces and, in particular, we prove a characterization of bounded $Q_p$-functions in terms of pointwise multipliers between such spaces. Moreover, we use our approach based on imbeddings in vector-valued sequence spaces to obtain atomic... (More)
Summary: In [Aleman, A., Carlsson, M. and Persson A., Preduals of $Q_p$-spaces. Complex Variables (To appear).], we have obtained a representation of the Cauchy-predual of the space $Q_p$ on the unit disc as a weak product of weighted Dirichlet and Bergman spaces. The present article is a continuation of Aleman et al. and contains several applications and further developments of those results. We investigate the relation between $Q_p$ and Carleson inequalities for functions in weighted Dirichlet spaces and, in particular, we prove a characterization of bounded $Q_p$-functions in terms of pointwise multipliers between such spaces. Moreover, we use our approach based on imbeddings in vector-valued sequence spaces to obtain atomic decompositions of the predual of $Q_p$. This last result is then extended to the real variable setting where we prove atomic decomposition theorems for the preduals of certain function spaces that generalize $Q_p(mathbb R^n)$. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Complex Variables and Elliptic Equations
volume
52
issue
7
pages
629 - 653
publisher
Taylor & Francis
ISSN
1747-6933
language
English
LU publication?
yes
id
d1953873-14a9-401d-be5e-9ce6aacc32e9 (old id 790682)
date added to LUP
2007-12-21 12:34:32
date last changed
2016-04-16 06:03:08
@article{d1953873-14a9-401d-be5e-9ce6aacc32e9,
  abstract     = {Summary: In [Aleman, A., Carlsson, M. and Persson A., Preduals of $Q_p$-spaces. Complex Variables (To appear).], we have obtained a representation of the Cauchy-predual of the space $Q_p$ on the unit disc as a weak product of weighted Dirichlet and Bergman spaces. The present article is a continuation of Aleman et al. and contains several applications and further developments of those results. We investigate the relation between $Q_p$ and Carleson inequalities for functions in weighted Dirichlet spaces and, in particular, we prove a characterization of bounded $Q_p$-functions in terms of pointwise multipliers between such spaces. Moreover, we use our approach based on imbeddings in vector-valued sequence spaces to obtain atomic decompositions of the predual of $Q_p$. This last result is then extended to the real variable setting where we prove atomic decomposition theorems for the preduals of certain function spaces that generalize $Q_p(mathbb R^n)$.},
  author       = {Aleman, Alexandru and Carlsson, Marcus and Persson, Anna-Maria},
  issn         = {1747-6933},
  language     = {eng},
  number       = {7},
  pages        = {629--653},
  publisher    = {Taylor & Francis},
  series       = {Complex Variables and Elliptic Equations},
  title        = {Preduals of $Q_p$-spaces. II: Carleson imbeddings and atomic decompositions},
  volume       = {52},
  year         = {2007},
}