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

 

A weak-type orthogonality principle


Authors: Jose Barrionuevo and Michael T. Lacey
Journal: Proc. Amer. Math. Soc. 131 (2003), 1763-1769
MSC (2000): Primary 42B25
Published electronically: September 19, 2002
MathSciNet review: 1955263
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Abstract: We prove a weak type estimate for operators of the form $ f \to \sum_{s\in\mathbf S}\langle f,\varphi s \rangle \varphi s $ for certain collections of Schwartz functions $\{ \varphi s \}_{s\in\mathbf S}$. This extends some of the orthogonality issues involved in the study of the bilinear Hilbert transform by Lacey and Thiele.


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Additional Information

Jose Barrionuevo
Affiliation: Department of Mathematics and Statistics, University of South Alabama, Mobile, Alabama 36688
Email: jose@jaguar1.usouthal.edu

Michael T. Lacey
Affiliation: School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332
Email: lacey@math.gatech.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06744-8
PII: S 0002-9939(02)06744-8
Received by editor(s): January 10, 2002
Published electronically: September 19, 2002
Additional Notes: The second author was supported by NSF grant DMS–9706884
Communicated by: Andreas Seeger
Article copyright: © Copyright 2002 American Mathematical Society