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

(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)

Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/790682

- author
- Aleman, Alexandru
^{LU}; Carlsson, Marcus^{LU}and Persson, Anna-Maria^{LU} - organization
- publishing date
- 2007
- 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
- 2016-04-04 08:53:53
- date last changed
- 2018-11-21 20:50:00

@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}, }