On bilinear Littlewood-Paley square functions
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- by P. K. Ratnakumar and Saurabh Shrivastava PDF
- Proc. Amer. Math. Soc. 140 (2012), 4285-4293 Request permission
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 $\mathbb {T}^d.$References
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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
- MR Author ID: 894393
- Email: saurabhkumar@hri.res.in
- Received by editor(s): June 4, 2011
- Published electronically: April 27, 2012
- Communicated by: Michael T. Lacey
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 140 (2012), 4285-4293
- MSC (2010): Primary 42A45, 42B15, 42B25
- DOI: https://doi.org/10.1090/S0002-9939-2012-11349-8
- MathSciNet review: 2957219