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Parameterized Littlewood-Paley operators and area integrals on weak hardy spaces

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Abstract

In this paper, we establish the boundedness of parameterized Littlewood-Paley operator μ *,ρλ and parameterized area integral μ ρΩ,S with kernel satisfying the logarithmic type Lipschitz condition on the weak Hardy space.

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References

  1. Ding, Y., Lu, S. Z., Xue, Q. Y.: Parametrized area integrals on Hardy spaces and weak Hardy spaces. Acta Math. Sin., Engl. Ser., 23(9), 1537–1552 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  2. Ding, Y., Lu, S. Z., Xue, Q. Y.: Parametrized Littlewood-Paley operators on Hardy and weak Hardy spaces. Math. Nachr., 280(4), 351–363 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  3. Ding, Y., Lu, S. Z., Yabuta, K.: A problem on rough parametric Macinkiewicz functions. J. Austral. Math. Soc. (A), 72, 13–21 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  4. Duoandikoetxea, J., Seijo, E.: Weighted inequalities for rough square functions through extrapolation. Studia Math., 149, 239–252 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  5. Fefferman, R., Soria, F.: The weak spaces H1. Studia Math., 85, 1–16 (1987)

    MathSciNet  Google Scholar 

  6. Hörmander, L.: Estimates for translation invariant operators in L p spaces. Acta Math., 104, 93–140 (1960)

    Article  MathSciNet  MATH  Google Scholar 

  7. Lee, J., Rim, K. S.: Estimates of Marcinkiewicz integral with bounded homogeneous kernel of degree zero. Integral Equations Operator Theory, 48, 213–223 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  8. Lin, Y., Liu, Z. G., Gao, F. L.: Endpoint estimates for parametrized Littlewood-Paley operator. Commun. Math. Anal., 12(2), 11–25 (2012)

    MathSciNet  MATH  Google Scholar 

  9. Sakamoto, M., Yabuta, K.: Boundedness of Marcinkiewicz functions. Studia Math., 135, 103–142 (1999)

    MathSciNet  MATH  Google Scholar 

  10. Stein, E. M.: Sigular Integral and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, New Jersey, 1970

    Google Scholar 

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Authors and Affiliations

  1. School of Sciences, China University of Mining and Technology, Beijing, 100083, P. R. China

    Yan Lin, Zong Guang Liu, Dong Lan Mao & Zhen Kai Sun

Authors
  1. Yan Lin
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  2. Zong Guang Liu
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  3. Dong Lan Mao
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  4. Zhen Kai Sun
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Correspondence to Yan Lin.

Additional information

Supported by National Natural Science Foundation of China (Grant Nos. 11001266 and 11171345) and Fundamental Research Funds for the Central Universities (Grant No. 2009QS16)

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Lin, Y., Liu, Z.G., Mao, D.L. et al. Parameterized Littlewood-Paley operators and area integrals on weak hardy spaces. Acta. Math. Sin.-English Ser. 29, 1857–1870 (2013). https://doi.org/10.1007/s10114-013-2440-5

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  • DOI: https://doi.org/10.1007/s10114-013-2440-5

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