Available in electronic format
Available in print format		 Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(e) ISSN 0002-9947(p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

Truncations of multilinear Hankel operators

Author(s): Aline Bonami; Sandrine Grellier; Mohammad Kacim
Journal: Trans. Amer. Math. Soc. 360 (2008), 1377-1390.
MSC (2000): Primary 47B35; Secondary 42A50, 47A63, 47B10, 47B49
Posted: October 3, 2007
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

Abstract: We extend to multilinear Hankel operators the fact that some truncations of bounded Hankel operators are still bounded. We prove and use a continuity property of bilinear Hilbert transforms on products of Lipschitz spaces and Hardy spaces.

References:

[BB]
Bonami, A. and Bruna, J. On truncations of Hankel and Toeplitz operators. Publ. Mat. 43 no. 1, 235-250 (1999). MR 1697523 (2000c:47046)

[BL]
Bergh, J. and Löfström, J. Interpolation spaces. An introduction. Grundlehren der Mathematischen Wissenschaften, No. 223. Springer-Verlag, Berlin-New York, 207 pp (1976). MR 0482275 (58:2349)

[CM]
Coifman, R.R. and Meyer, Y. On commutators of singular integrals and bilinear singular integrals, Trans. Am. Math. Soc., 212, 315-331 (1975). MR 0380244 (52:1144)

[CW]
Coifman, R. R. and Weiss, G. Transference methods in analysis. Conference Board of the Mathematical Sciences Regional Conference Series in Mathematics, No. 31. American Mathematical Society, Providence, R.I., (1976). MR 0481928 (58:2019)

[D]
Duren, P. L. Theory of $ H\sp{p}$ spaces. Pure and Applied Mathematics, Vol. 38 Academic Press, New York-London 258 pp (1970). MR 0268655 (42:3552)

[GR]
García-Cuerva, J. and Rubio de Francia, J. L. Weighted norm inequalities and related topics. North-Holland Mathematics Studies, 116. Notas de Matemática [Mathematical Notes], 104. North-Holland Publishing Co., Amsterdam, 604 pp (1985). MR 0807149 (87d:42023)

[GB]
Gasch, J.E. and Gilbert, J. E. Triangularization of Hankel operators and the bilinear Hilbert transform, Contemp. Math., 247, 235-248, (1999). MR 1738092 (2001b:47044)

[GraK]
Grafakos, L. and Kalton, N. Multilinear Calderón-Zygmund operators on Hardy spaces, Collect. Math., 52 (2), 169-179 (2001). MR 1852036 (2002k:42032)

[GraL]
Grafakos, L. and Li, X. Uniform bounds for the bilinear Hilbert transforms. I. Ann. of Math. (2) 159 (2004), no. 3, 889-933. MR 2113017 (2006e:42011)

[GraT]
Grafakos, L. and Torres, R.H. Multilinear Calderón-Zygmund theory, Adv. in Math., 165, 124-164 (2002). MR 1880324 (2002j:42029)

[GreK]
Grellier, S. and Kacim, M. Truncation of multilinear Hankel operators, preprint (2003).

[KS]
Kenig, C.E. and Stein, E.M. Multilinear estimates and fractional integration, Math. Research Lett., 6, 1-15 (1999). MR 1682725 (2000k:42023a)

[L]
Lacey, M. The bilinear maximal function maps in $ L^p$ for $ 2/3< p \leq 1$, Ann. of Math., 151(2), 35-57 (2000). MR 1745019 (2001b:42015)

[LT1]
Lacey, M. and Thiele, C. $ L^p$ estimates on the bilinear Hilbert transform, $ 2< p< \infty$, Ann. of Math., 146, 683-724 (1997). MR 1491450 (99b:42014)

[LT2]
Lacey, M. and Thiele, C. M. On Calderón's conjecture for the bilinear Hilbert transform. Proc. Natl. Acad. Sci. USA 95 , no. 9, 4828-4830 (1998) MR 1619285 (99e:42013)

[LT3]
Lacey, M. and Thiele, C. On Calderón's conjecture, Annals of Math., 149, 475-496 (1999). MR 1689336 (2000d:42003)

[MTT]
Muscalu, C., Tao, T. and Thiele, C. Multilinear operators given by singular multipliers, J. Am. Math. Soc., 15, 469-496 (2002). MR 1887641 (2003b:42017)

[S]
Stein, E.M. Harmonic Analysis: Real Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton University Press, Princeton, NJ (1993). MR 1232192 (95c:42002)

Similar Articles:

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 47B35, 42A50, 47A63, 47B10, 47B49

Retrieve articles in all Journals with MSC (2000): 47B35, 42A50, 47A63, 47B10, 47B49

Additional Information:

Aline Bonami
Affiliation: MAPMO, Université d'Orléans, Faculté des Sciences, Département de Mathématiques, BP 6759, F 45067 Orleans Cédex 2, France
Email: bonami@labomath.univ-orleans.fr

Sandrine Grellier
Affiliation: MAPMO, Université d'Orléans, Faculté des Sciences, Département de Mathématiques, BP 6759, F 45067 Orleans Cédex 2, France
Email: grellier@labomath.univ-orleans.fr

Mohammad Kacim
Affiliation: Université Saint-Joseph, Rue de Damas, Beirut 1104-2020, Lebanon
Email: kacim76@hotmail.com

DOI: 10.1090/S0002-9947-07-04185-2
PII: S 0002-9947(07)04185-2
Keywords: Hankel operator, truncation, Hardy spaces, Lipschitz spaces, bilinear Hilbert transform
Received by editor(s): November 22, 2004
Received by editor(s) in revised form: October 7, 2005
Posted: October 3, 2007
Additional Notes: The authors were partially supported by the 2002-2006 IHP Network, Contract Number: HPRN-CT-2002-00273 - HARP
The authors would like to thank Joaquim Bruna who suggested this problem.
Copyright of article: Copyright 2007, American Mathematical Society

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google