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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1039533-0
PII: S 0002-9939(1991)1039533-0
Keywords: Hardy and weighted Bergman spaces, Carleson measures, polydiscs
Article copyright: © Copyright 1991 American Mathematical Society