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New Weighted Norm Inequalities for Certain Classes of Multilinear Operators and their Iterated Commutators

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  • Published: 09 April 2015
  • Volume 43, pages 371–398 (2015)
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New Weighted Norm Inequalities for Certain Classes of Multilinear Operators and their Iterated Commutators
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  • Guixia Pan1 &
  • Lin Tang2 
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Abstract

Applying the new class of multiple weights functions and new sharp maximal functions, we obtain the pointwise estimates, strong type and weak end-point estmates for certain classes of multilinear operators and their iterated commutators with new BMO functions.

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References

  1. Bényi, Á., Torres, R.: Symbolic calculus and the transposes of bilinear pseudodifferential operators. Comm. Par. Diff. Eq 28, 1161–1181 (2003)

    Article  MATH  Google Scholar 

  2. Bui, T.A.: New class of multiple weights and new weighted inequalities for multilinear operators, to appear in Forum Math (arXiv:1203.2797(2012))

  3. Bongioanni, B., Haboure, E., Salinas, O.: Commutators of Riesz transforms related to Schrödinger operators. J. Fourier Anal. Appl 17, 115–134 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bongioanni, B., Haboure, E., Salinas, O.: Classes of weights related to Schrödinger operators. J. Math. Anal. Appl 373, 563–579 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  5. Coifman, R., Rochberg, R., Weiss, G.: Factorization theorems for Hardy spaces in several variables. Ann. of Math. 103, 611–635 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  6. García-Cuerva, J., Rubio de Francia, J.: Weighted Norm Inequalities and Related Topics. Amsterdam- New York, North-Holland (1985)

  7. Grafakos, L., Torres, R.H.: Multilinear Calderón-Zygmund theory. Adv. Math 165(1), 124–164 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  8. Lerner, A.K., Ombrosi, S., Pérez, C., Torres, R.H., Trujillo-González, R.: New maximal functions and multiple weights for the multilinear Calderón-Zygmund theory. Adv. Math 220(4), 1222–1264 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  9. Pérez, C.: Endpoint estimates for commutators of singular integrals. J. Funct Anal 128, 163–185 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  10. Pérez, C., Pradolini, G.: Sharp weighted endpoint estimates for commutators of singular integral operators. Michigan Math. J 49, 23–37 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  11. Pérez, C., Pradolini, G., Torres, R., Trujillo-Gonzalez, R.: End-point estimates for iterated commutators of multilinear singular integrals. Bull. London Math. Soc 46, 26–42 (2014)

    Article  MATH  Google Scholar 

  12. Pérez, C., Torres, R.: Sharp maximal function estimates for multilinear singular integrals. Contemp. Math. 320, 323–331 (2003)

    Article  Google Scholar 

  13. Tang, L.: Weighted norm inequalities for pseudo-differential operators with smooth symbols and their commutators. J. Funct. Anal 262, 1603–1629 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  14. Tang, L., from, Extrapolation: \(A^{\rho ,\infty }_{\infty }\), Vector-valued inequalities and applications in Schrödinger settings. Ark. Mat 52, 175–202 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  15. Wilson, M.: Weighted Littlewood-Paley Theory and Exponential-Square Integrability, Lecture Notes in Math, vol. 1924. Springer, Berlin (2008)

    Google Scholar 

  16. Rao, M.M., Ren, Z.D.: Theory of Orlicz Spaces. Marcel Dekker, New York (1991)

    MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. School of Public Health, Anhui Medical University, Anhui, 230032, People’s Republic of China

    Guixia Pan

  2. LMAM, School of Mathematical Sciences, Peking University, Beijing, 100871, People’s Republic of China

    Lin Tang

Authors
  1. Guixia Pan
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  2. Lin Tang
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Corresponding author

Correspondence to Lin Tang.

Additional information

The research was supported by the NNSF (11271024) of China.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

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Cite this article

Pan, G., Tang, L. New Weighted Norm Inequalities for Certain Classes of Multilinear Operators and their Iterated Commutators. Potential Anal 43, 371–398 (2015). https://doi.org/10.1007/s11118-015-9477-2

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  • Received: 07 June 2012

  • Accepted: 22 March 2015

  • Published: 09 April 2015

  • Issue date: October 2015

  • DOI: https://doi.org/10.1007/s11118-015-9477-2

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Keywords

  • Multilinear operator
  • Multiple weight

Mathematics Subject Classification (2010)

  • 42B25
  • 42B20

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