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

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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 $Q_p(mathbb R^n)$.

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Subject classification (UKÄ) – MANDATORY

  • Mathematics
Original languageEnglish
Pages (from-to)629-653
JournalComplex Variables and Elliptic Equations
Volume52
Issue number7
Publication statusPublished - 2007
Publication categoryResearch
Peer-reviewedYes