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Quantitative weighted bounds for the vector-valued singular integral operators with nonsmooth kernels

Guoen Hu
대한수학회 (The Korean Mathematical Society)|2018.11|대한수학회보 (Bulletin of the KMS)|제55권 제6호|pp. 1791-1809

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참고문헌

키워드

singular integral operatorweighted boundnonsmooth kernelsparse operatorsharp maximal operator
주제분류수학

초록

Let $T$ be the singular integral operator with nonsmooth kernel which was introduced by Duong and McIntosh, and $T_q$ ($q\in (1,\,\infty))$ be the vector-valued operator defined by $T_qf(x)=\big(\sum_{k=1}^{\infty}|Tf_k(x)|^q\big)^{1/q}$. In this paper, by proving certain weak type endpoint estimate of $L\log L$ type for the grand maximal operator of $T$, the author establishes some quantitative weighted bounds for $T_q$ and the corresponding vector-valued maximal singular integral operator.

Abstract

Let $T$ be the singular integral operator with nonsmooth kernel which was introduced by Duong and McIntosh, and $T_q$ ($q\in (1,\,\infty))$ be the vector-valued operator defined by $T_qf(x)=\big(\sum_{k=1}^{\infty}|Tf_k(x)|^q\big)^{1/q}$. In this paper, by proving certain weak type endpoint estimate of $L\log L$ type for the grand maximal operator of $T$, the author establishes some quantitative weighted bounds for $T_q$ and the corresponding vector-valued maximal singular integral operator.

참고문헌 (25)

  1. S. M. Buckley, "Estimates for operator norms on weighted spaces and reverse Jensen inequalities", Trans. Amer. Math. Soc, 340(1), pp.253~272 (1993)
  2. M. Carozza, "Di Napoli, Composition of maximal operators", Publ. Mat, 40(2), pp.397~409 (1996)
  3. Jiecheng Chen, "Weighted vector-valued bounds for a class of multilinear singular integral operators and applications", 대한수학회지, 55(3), pp.671~694 (2018), 대한수학회
  4. D. Cruz-Uribe, "Sharp weighted estimates for classical operators", Adv. Math, 229(1), pp.408~441 (2012)
  5. O. Dragicevic, "Extrapolation and sharp norm estimates for classical operators on weighted Lebesgue spaces", Publ. Mat, 49(1), pp.73~91 (2005)
  6. X. T. Duong, "Singular integral operators with non-smooth kernels on irregular domains", Rev. Mat. Iberoamericana, 15(2), pp.233~265 (1999)
  7. C. Fefferman, "Some maximal inequalities", Amer. J. Math, 93, pp.107~115 (1971)
  8. L. Grafakos, "Modern Fourier Analysis" (2009), Springer
  9. G. Hu, "Weighted vector-valued estimates for a non-standard Calderon-Zygmund opera-tor", Nonlinear Anal, 165, pp.143~162 (2017)
  10. G. Hu, "Weighted estimates for singular integral operators with nonsmooth kernels and applications", J. Aust. Math. Soc, 85(3), pp.377~417 (2008)
  11. T. Hytonen, "The sharp weighted bound for general Calderon-Zygmund operators", Ann. of Math., 175(3), pp.1473~1506 (2012)
  12. T. Hytonen, "Sharp weighted bounds for the q-variation of singular integrals", Bull. Lond. Math. Soc, 45(3), pp.529~540 (2013)
  13. T. Hytonen, "Sharp weighted bounds involving A1", Anal. PDE, 6(4), pp.777~818 (2013)
  14. T. Hytonen, "The L(log L)є endpoint estimate for maximal singular integral operators", J. Math. Anal. Appl, 428(1), pp.605~626 (2015)
  15. M. T. Lacey, "On Ap-A1 type estimates for square functions", Math. Z, 284(3-4), pp.1211~1222 (2016)
  16. H. V. Le, "Vector-valued singular integrals with non-smooth kernels on spaces of homo-geneous type", Complex Anal. Oper. Theory, 11(1), pp.57~84 (2017)
  17. A. K. Lerner, "On pointwise estimates involving sparse operators", New York J. Math, 22, pp.341~349 (2016)
  18. A. K. Lerner, "On pointwise and weighted estimates for commutators of Calderon-Zygmund operators", Adv. Math, 319, pp.153~181 (2017)
  19. J. M. Martell, "Sharp maximal functions associated with approximations of the identity in spaces of homogeneous type and applications", Studia Math, 161(2), pp.113~145 (2004)
  20. H. -X. Mo, "Vector-valued singular integral operators with non-smooth ker-nels and related multilinear commutators", Pure Appl. Math. Q, 3(2, Special Issue: In honor of Leon Simon. Part 1), pp.451~480 (2007)
  21. C. Perez, "Weighted norm inequalities for singular integral operators", J. London Math. Soc. (2), 49(2), pp.296~308 (1994)
  22. S. Petermichl, "The sharp bound for the Hilbert transform on weighted Lebesgue spaces in terms of the classical Ap characteristic", Amer. J. Math, 129(5), pp.1355~1375 (2007)
  23. S. Petermichl, "The sharp weighted bound for the Riesz transforms", Proc. Amer. Math. Soc, 136(4), pp.1237~1249 (2008)
  24. E. M. Stein, "Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals" (1993), Princeton University Press
  25. J. M. Wilson, "Weighted inequalities for the dyadic square function without dyadic A1", Duke Math. J, 55(1), pp.19~50 (1987)

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