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

 

Weak-star convergence in multiparameter Hardy spaces


Authors: Jill Pipher and Sergei Treil
Journal: Proc. Amer. Math. Soc. 139 (2011), 1445-1454
MSC (2010): Primary 42B30, 42B35
Published electronically: September 3, 2010
MathSciNet review: 2748438
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Abstract: We prove a multiparameter version of a classical theorem of Jones and Journé on weak-star convergence in the Hardy space $ H^1$.


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Additional Information

Jill Pipher
Affiliation: Department of Mathematics, Brown University, 151 Thayer Street, Box 1917, Providence, Rhode Island 02912

Sergei Treil
Affiliation: Department of Mathematics, Brown University, 151 Thayer Street, Box 1917, Providence, Rhode Island 02912
Email: treil@math.brown.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10567-1
PII: S 0002-9939(2010)10567-1
Keywords: Weak-star convergence, multiparameter Hardy space, VMO
Received by editor(s): February 5, 2010
Received by editor(s) in revised form: May 3, 2010
Published electronically: September 3, 2010
Additional Notes: The first author is supported by the NSF grant DMS-0901139
The second author is supported by the NSF grant DMS-0800876.
Communicated by: Michael T. Lacey
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.