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

   

 

On bilinear Littlewood-Paley square functions


Authors: P. K. Ratnakumar and Saurabh Shrivastava
Journal: Proc. Amer. Math. Soc. 140 (2012), 4285-4293
MSC (2010): Primary 42A45, 42B15, 42B25
Published electronically: April 27, 2012
MathSciNet review: 2957219
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Abstract: In this paper, we study the bilinear Littlewood-Paley square function introduced by M. Lacey. We give an easy proof of its boundedness from $ L^p(\mathbb{R}^d) \times L^q(\mathbb{R}^d)$ into $ L^r(\mathbb{R}^d),~d\geq 1,$ for all possible values of exponents $ p,q,r,$ i.e. for $ 2\leq p,q\leq \infty ,~1\leq r\leq \infty $ satisfying $ \frac {1}{p}+\frac {1}{q}= \frac {1}{r}$. We also prove analogous results for bilinear square functions on the torus group $ \mathbb{T}^d.$


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Additional Information

P. K. Ratnakumar
Affiliation: School of Mathematics, Harish-Chandra Research Institute, Allahabad, India
Email: ratnapk@hri.res.in

Saurabh Shrivastava
Affiliation: School of Mathematics, Harish-Chandra Research Institute, Allahabad, India
Email: saurabhkumar@hri.res.in

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11349-8
Keywords: Bilinear multipliers, Littlewood-Paley square functions
Received by editor(s): June 4, 2011
Published electronically: April 27, 2012
Communicated by: Michael T. Lacey
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.