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 | References | Similar Articles | Additional Information
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 using what one may characterize as the bounded identity operators from Hardy spaces of polydiscs in
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
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:
https://doi.org/10.1090/S0002-9939-1991-1039533-0
Keywords:
Hardy and weighted Bergman spaces,
Carleson measures,
polydiscs
Article copyright:
© Copyright 1991
American Mathematical Society