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Singular integral operators on product domains along twisted surfaces

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Abstract

We introduce a class of singular integral operators on product domains along twisted surfaces. We prove that the operators are bounded on Lp provided that the kernels satisfy weak conditions.

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References

  1. Al-Qassem H, Al-Salman A. Lp Boundedness of a class of singular integral operators with rough kernels. Turkish J Math, 2001, 25(4): 519–533

    MathSciNet  MATH  Google Scholar 

  2. Al-Qassem H, Pan Y. Lp boundedness for singular integrals with rough kernels on product domains. Hokkaido Math J, 2002, 31: 555–613

    Article  MathSciNet  Google Scholar 

  3. Al-Salman A, Al-Qassem H, Pan Y. Singular integrals on product domains. Indiana Univ Math J, 2006, 55(1): 369–387

    Article  MathSciNet  Google Scholar 

  4. Al-Salman A, Pan Y. Singular integrals with rough kernels in Llog+L(Sn−1). J Lond Math Soc (2), 2002, 66:: 153–174

    Article  Google Scholar 

  5. Duoandikoetxea J. Multiple singular integrals and maximal functions along hypersurfaces. Ann Inst Fourier (Grenoble), 1986, 36: 185–206

    Article  MathSciNet  Google Scholar 

  6. Fan D, Guo K, Pan Y. Singular integrals with rough kernels on product spaces. Hokkaido Math J, 1999, 28: 435–460

    Article  MathSciNet  Google Scholar 

  7. Fan D, Pan Y. Singular integral operators with rough kernels supported by subvarieties. Amer J Math, 1997, 119: 799–839

    Article  MathSciNet  Google Scholar 

  8. Fefferman R. Singular integrals on product domains. Bull Amer Math Soc, 1981, 4: 195–201

    Article  MathSciNet  Google Scholar 

  9. Fefferman R, Stein E M. Singular integrals on product spaces. Adv Math, 1982, 45: 117–143

    Article  MathSciNet  Google Scholar 

  10. Jiang Y, Lu S. A class of singular integral operators with rough kernels on product domains. Hokkaido Math J, 1995, 24: 1–7

    Article  MathSciNet  Google Scholar 

  11. Keitoku M, Sato E. Block spaces on the unit sphere in Rn. Proc Amer Math Soc, 1993, 119: 453–455

    MathSciNet  MATH  Google Scholar 

  12. Stein E M. Harmonic Analysis: Real-Variable Methods, Orthogonality and Oscillatory Integrals. Princeton Math Ser, 43. Princeton: Princeton Univ Press, 1993

    MATH  Google Scholar 

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Acknowledgements

The author would like to thank the anonymous referee for the very valuable comments on the first version of the paper. Reviewer comments have led to substantial improvement of the presentation of the paper.

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Authors and Affiliations

  1. Department of Mathematics, Sultan Qaboos University, Sultanate, Oman

    Ahmad Al-Salman

  2. Department of Mathematics, Yarmouk University, Irbid, Jordan

    Ahmad Al-Salman

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  1. Ahmad Al-Salman
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Correspondence to Ahmad Al-Salman.

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Al-Salman, A. Singular integral operators on product domains along twisted surfaces. Front. Math. China 16, 13–28 (2021). https://doi.org/10.1007/s11464-021-0911-z

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  • DOI: https://doi.org/10.1007/s11464-021-0911-z

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