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A weak-type orthogonality principle

Author(s): Jose Barrionuevo; Michael T. Lacey
Journal: Proc. Amer. Math. Soc. 131 (2003), 1763-1769.
MSC (2000): Primary 42B25
Posted: September 19, 2002
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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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M.T. Lacey. ``The bilinear Hilbert transform is pointwise finite." Rev. Mat. 13 (1997) 403--469. MR 99j:42009

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M.T. Lacey and C.M. Thiele. ``$L^p$ estimates for the bilinear Hilbert transform on $L^p$." Proc. Nat. Acad. Sci. 94 (1997) 33--35. MR 98e:44001

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M.T. Lacey and C.M. Thiele. ``$L^p$ estimates for the bilinear Hilbert transform, $p>2$." Ann. Math. 146 (1997) 693--724. MR 99b:42014

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F.G. Meyer and R.R. Coifman. ``Brushlets: A tool for directional image analysis and image compression." Appl. Comp. Harmonic Anal. 4 (1997) 147--187. MR 99c:42069

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E. Prestini. ``On the two proof of pointwise convergence of Fourier series." Amer. J. Math. 104 (1982) 127--139. MR 83i:42005

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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: 10.1090/S0002-9939-02-06744-8
PII: S 0002-9939(02)06744-8
Received by editor(s): January 10, 2002
Posted: September 19, 2002
Additional Notes: The second author was supported by NSF grant DMS--9706884
Communicated by: Andreas Seeger
Copyright of article: Copyright 2002, American Mathematical Society

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