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PARABOLIC MARCINKIEWICZ INTEGRALS ASSOCIATED TO POLYNOMIALS COMPOUND CURVES AND EXTRAPOLATION

Daiqing Zhang|Feng Liu
대한수학회 (The Korean Mathematical Society)|2015.05|대한수학회보 (Bulletin of the KMS)|제52권 제3호|pp. 771-788

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참고문헌

키워드

extrapolationrough kernelsMarcinkiewicz integralsmixed homogeneity
주제분류수학

초록

In this note we consider the parametric Marcinkiewicz integrals with mixed homogeneity along polynomials compound curves. Under the rather weakened size conditions on the integral kernels both on the unit sphere and in the radial direction, the Lp bounds of such operators are given by an extrapolation argument. Some previous results are greatly extended and improved.

Abstract

In this note we consider the parametric Marcinkiewicz integrals with mixed homogeneity along polynomials compound curves. Under the rather weakened size conditions on the integral kernels both on the unit sphere and in the radial direction, the Lp bounds of such operators are given by an extrapolation argument. Some previous results are greatly extended and improved.

참고문헌 (28)

  1. H. Al-Qassem, "On certain rough integral operators and ex-trapolation", J. Inequal. Pure Appl. Math, 10(3), pp.15~ (2009)
  2. H. Al-Qassem, "On certain estimates for Marcinkiewicz integrals and extrap-olation", Collect. Math, 60(2), pp.123~145 (2009)
  3. A. Al-Salman, "A note on parabolic Marcinkiewicz integrals along surfaces", Proc. A. Razmadze Math. Inst, 154, pp.21~36 (2010)
  4. A. Al-Salman, "On the L2 boundedness of parametric Marcinkiewicz integral operator", J. Math. Anal. Appl, 375(2), pp.745~752 (2011)
  5. A. Al-Salman, "Lp bounds for the function of Marcinkiewicz", Math. Res. Lett, 9(5-6), pp.697~700 (2002)
  6. A. P. Calder´on, "Parabolic maximal functions associated with a dis-tribution", Adv. in Math, 16, pp.1~64 (1975)
  7. Y. Chen, "Lp bounds for the parabolic Marcinkiewicz integral with rough kernels", 대한수학회지, 44(3), pp.733~745 (2007), 대한수학회
  8. Y. Chen, "The parabolic Littlewood-Paley operator with Hardy space kernels", Canad. Math. Bull, 52(4), pp.521~534 (2009)
  9. Y. Ding, "Lp-boundedness of Marcinkiewicz integrals with Hardy space function kernel", Acta Math. Sin. (Engl. Ser.), 16(4), pp.593~600 (2000)
  10. Y. Ding, "On the Lp boundedness of Marcinkiewicz integrals", Michigan Math. J, 50(1), pp.17~26 (2002)
  11. Y. Ding, "A problem on rough parametric Marcinkiewicz functions", J. Aust. Math. Soc, 72(1), pp.13~21 (2002)
  12. Y. Ding, "A remark to the L2 boundedness of parametric Marcinkiewicz integral", J. Math. Anal. Appl, 387(2), pp.691~697 (2012)
  13. Y. Ding, "Boundedness of the Marcinkiewicz integrals with rough kernel associated to surfaces", Tohoku Math. J, 62(2), pp.233~262 (2010)
  14. J. Duoandikoetxea, "Maximal and singular integral operators via Fourier transform estimates", Invent. Math, 84, pp.541~561 (1986)
  15. E. Fabes, "Singular integrals with mixed homogeneity", Studia Math, 27, pp.19~38 (1966)
  16. D. Fan, "Singular integral operators with rough kernels supported by subva-rieties", Amer. J. Math, 119(4), pp.799~839 (1997)
  17. L. H¨ormander, "Estimates for translation invariant operators in Lp spaces", Acta Math, 104, pp.93~104 (1960)
  18. F. Liu, "On singular integrals associated to surfaces", Tohoku Math. J, 66(1), pp.1~14 (2014)
  19. F. Liu, "Rough Marcinkiewicz integrals with mixed homogeneity on product spaces", Acta Math. Sin. (Engl. Ser.), 29(7), pp.1231~1244 (2013)
  20. W. R. Madych, "On Littlewood-Paley functions", Studia Math, 50, pp.43~63 (1974)
  21. M. Sakamoto, "Boundedness of Marcinkiewicz functions", Studia Math, 135(2), pp.103~142 (1999)
  22. S. Sato, "Estimates for singular integrals and extrapolation", Studia Math, 192(3), pp.219~233 (2009)
  23. E. M. Stein, "On the function of Littlewood-Paley, Lusin and Marcinkiewicz", Trans. Amer. Math. Soc, 88, pp.430~466 (1958)
  24. T. Walsh, "On the function of Marcinkiewicz", Studia Math, 44, pp.203~217 (1972)
  25. Feixing Wang, "Lp bounds for the parabolic Littlewood-Paley operator associated to surfaces of revolution", 대한수학회보, 49(4), pp.787~797 (2012), 대한수학회
  26. H. Wu, "On Marcinkiewicz integral operator with rough kernels", Integral Equations Operator Theory, 52(2), pp.285~298 (2005)
  27. H. Wu, "Lp bounds for Marcinkiewicz integrals associates to surfaces of revolution", J. Math. Anal. Appl, 321(2), pp.811~827 (2006)
  28. Q. Xue, "Parabolic Littlewood-Paley g-function with rough kernel", Acta Math. Sin. (Engl. Ser.), 24(12), pp.2049~2060 (2008)

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