Carleson measures in Hardy and weighted Bergman spaces of polydiscs

Jafari, F.

doi:10.1090/S0002-9939-1991-1039533-0

Carleson measures in Hardy and weighted Bergman spaces of polydiscs

Author: F. Jafari
Journal: Proc. Amer. Math. Soc. 112 (1991), 771-781
MSC: Primary 47B38; Secondary 32A35, 46E15, 47B07
DOI: https://doi.org/10.1090/S0002-9939-1991-1039533-0
MathSciNet review: 1039533
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Abstract: The importance of theorems on Carleson measures has been well recognized [3]. In [1] Chang has given a characterization of the bounded measures on ${L^p}({T^n})$ using what one may characterize as the bounded identity operators from Hardy spaces of polydiscs in ${L^p}$ spaces. In [4] Hastings gives a similar result for (unweighted) Bergman spaces of polydiscs. In this paper we characterize the bounded identity operators from weighted Bergman spaces of polydiscs into ${L^p}$ spaces, and classify those operators which are compact on the Hardy and weighted Bergman spaces in terms of Carleson-type conditions. We give two immediate applications of these results here, and a much broader class of applications elsewhere [5].

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