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Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

A note on the bilinear Littlewood-Paley square function

Author(s): Parasar Mohanty; Saurabh Shrivastava
Journal: Proc. Amer. Math. Soc. 138 (2010), 2095-2098.
MSC (2000): Primary 42A45, 42B15, 42B25
Posted: January 29, 2010
MathSciNet review: 2596047
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Abstract | References | Similar articles | Additional information

Abstract: In this paper, we give an elementary proof of boundedness of the smooth bilinear Littlewood-Paley square function.

References:

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Bernicot, F., $ L^p$ estimates for non smooth bilinear Littlewood-Paley square functions on $ \mathbb{R}$, arXiv:0811.2854, to appear in Math. Ann.

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Lacey, M., On bilinear Littlewood-Paley square functions, Publ. Mat. 40 (1996), no. 2, 387-396. MR 1425626 (98c:42017)

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Lacey, M., The bilinear maximal functions map into $ L\sp p$ for $ 2/3<p\leq1$, Ann. of Math. (2) 151 (2000), no. 1, 35-57. MR 1745019 (2001b:42015)

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Lacey, M., Thiele, C., $ L^p$ estimates on the bilinear Hilbert transform for $ 2<p<\infty$, Ann. of Math. (2) 146 (1997), no. 3, 693-724. MR 1491450 (99b:42014)

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Lacey, M., Thiele, C., On Calderón's conjecture, Ann. of Math. (2) 149 (1999), no. 2, 475-496. MR 1689336 (2000d:42003)

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Rubio de Francia, J. L., Estimates for some square functions of Littlewood-Paley type, Publ. Sec. Mat. Univ. Autònoma Barcelona 27 (1983), no. 2, 81-108. MR 765844 (86d:42018)

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Rubio de Francia, J. L., A Littlewood-Paley inequality for arbitrary intervals, Rev. Mat. Iberoamericana 1 (1985), no. 2, 1-14. MR 850681 (87j:42057)

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Additional Information:

Parasar Mohanty
Affiliation: Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur-208016, India
Email: parasar@iitk.ac.in

Saurabh Shrivastava
Affiliation: Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur-208016, India
Email: saurabhk@iitk.ac.in

DOI: 10.1090/S0002-9939-10-10233-0
PII: S 0002-9939(10)10233-0
Keywords: Bilinear multiplier operators, Littlewood-Paley square function
Received by editor(s): September 25, 2009
Posted: January 29, 2010
Communicated by: Michael T. Lacey
Copyright of article: Copyright 2010, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.




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