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Lp Bounds for the Commutator of Parabolic Singular Integral with Rough Kernels

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Abstract

In this paper, the authors give the L p (1 < p < ∞ ) boundedness of the k-th order commutator of parabolic singular integral with the kernel function Ω ∈ L(log +  L)k + 1(S n − 1). The result in this paper is an extension of some known results.

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References

  1. Aguilera, N., Segovia, C.: Weighted norm inequalities relating the \(g_\lambda^*\) and the area functions. Studia Math. LXI, 293–303 (1977)

    MathSciNet  Google Scholar 

  2. Alvarez, J., Bagby, R., Kurtz, D., Pérez, C.: Weighted estimates for commutators of linear operators. Studia Math. 104, 195–209 (1993)

    MATH  MathSciNet  Google Scholar 

  3. Chen, Y., Ding, Y.: L p bounds for the parabolic Marcinkiewicz integral. J. Korean Math. Soc. 44, 733–745 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  4. Coifman, R., Rocherberg, R., Weiss, G.: Factorization theorems for Hardy spaces in several valuables. Ann. of Math. 103, 611–636 (1976)

    Article  MathSciNet  Google Scholar 

  5. Duoandikoetxea, J.: Fourier analysis. Grad. Stud. Math., AMS Providence, Rhode Island 29, 106 (2001)

  6. Fabes, E., Rivière, N.: Singular integrals with mixed homogeneity. Studia Math. 27, 19–38 (1966)

    MATH  MathSciNet  Google Scholar 

  7. Hu, G.: L 2(ℝn) boundedness for the commutators of convolution operators. Nagoya Math. J. 163, 55–70 (2001)

    MATH  MathSciNet  Google Scholar 

  8. Hu, G.: L p(ℝn) boundedness for the commutator of a homogeneous singular integral operator. Studia Math. 154, 13–27 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  9. Macías, R., Segovia, C.: Weighted norm inequalities for parabolic fractional integrals. Studia Math. T. LXI., 279–291 (1977)

    Google Scholar 

  10. Muckenhoupt, B.: Weighted norm inequalities for the Hardy maximal function. Trans. Amer. Math. Soc. 165, 207–226 (1972)

    Article  MATH  MathSciNet  Google Scholar 

  11. Palagachev, D., Softova, L.: Singular integral operators, Morrey spaces and fine regularity of solutions to PDE’s. Potential Anal. 20, 237–263 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  12. Stein, E.: Maximal functions: Homogeneous curves. Proc. Nat. Acad. Sci. U.S.A. 73, 2176–2177 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  13. Tozoni, S.: Weighted norm inequalities for vector-valued singular integrals on homogeneous spaces. Studia Math. 161, 71–97 (2004)

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China

    Yanping Chen & Yong Ding

  2. Applied Science School, University of Science and Technology Beijing, Beijing, 100083, China

    Yanping Chen

Authors
  1. Yanping Chen
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  2. Yong Ding
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Corresponding author

Correspondence to Yong Ding.

Additional information

The research was supported by NSF of China (Grant: 10571015) and SRFDP of China (Grant: 20050027025).

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Chen, Y., Ding, Y. Lp Bounds for the Commutator of Parabolic Singular Integral with Rough Kernels. Potential Anal 27, 313–334 (2007). https://doi.org/10.1007/s11118-007-9062-4

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  • DOI: https://doi.org/10.1007/s11118-007-9062-4

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