| Title | Preduals of $Q_p$-spaces. II: Carleson imbeddings and atomic decompositions |
| Authors | Alexandru Aleman, Marcus Carlsson, Anna-Maria Persson |
| Publication | Complex Var. Elliptic Equ. |
| Year | 2007 |
| Volume | 52 |
| Issue | 7 |
| Pages | 629 - 653 |
| Document type | Article |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Abstract English | 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 $Q_p(mathbb R^n)$. |
| ISBN/ISSN/Other | ISSN: 1747-6933, 1747-6941 |
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