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Parameterized Littlewood-Paley Operators and Area Integrals on Weak Hardy Spaces 被引量：2

Parameterized Littlewood-Paley Operators and Area Integrals on Weak Hardy Spaces
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摘要 In this paper, we establish the boundedness of parameterized Littlewood-Paley operator μλ^＊,p and parameterized area integralμΩ^σSp with kernel satisfying the logarithmic type Lipschitz condition on the weak Hardy space. In this paper, we establish the boundedness of parameterized Littlewood-Paley operator μλ^＊,p and parameterized area integralμΩ^σSp with kernel satisfying the logarithmic type Lipschitz condition on the weak Hardy space.
作者 Yan LIN Zong Guang LIU Dong Lan MAO Zhen Kai SUN
机构地区 School of Sciences
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2013年第10期1857-1870,共14页 数学学报（英文版）
基金 Supported by National Natural Science Foundation of China(Grant Nos.11001266 and 11171345) Fundamental Research Funds for the Central Universities(Grant No.2009QS16)
关键词 Parameterized Littlewood-Paley operator parameterized area integral weak Hardy space Parameterized Littlewood-Paley operator, parameterized area integral, weak Hardy space
分类号 O177 [理学—基础数学]
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参考文献10

  • 1Ding, 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).
  • 2Ding, Y., Lu, S. Z., Xue, Q. Y.: Parametrized Littlewood PMey operators on Hardy and weak Hardy spaces. Math. Nachr., 280(4), 351 363 (2007).
  • 3Ding, Y., Lu, S. Z., Yabuta, K.: A problem on rough parametric Macinkiewicz functions. J. Austral. Math. Soc. (A), 72, 13-21 (2002).
  • 4Duoandikoetxea, J., Seijo, E.: Weighted inequalities for rough square functions through extrapolation. Studia Math., 149, 239-252 (2002).
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  • 6HSrmander, L.: Estimates for translation invariant operators in Lp spaces. Acta Math., 104, 93-140 (1960).
  • 7Lee, J., Rim, K. S.: Estimates of Marcinkiewicz integral with bounded homogeneous kernel of degree zero. Integral Equations Operator Theory, 48, 213-223 (2004).
  • 8Lin, Y., Liu, Z. G., Gao, F. L.: Endpoint estimates for parametrized Littlewood-Paley operator. Commun. Math. Anal., 12(2), 11-25 (2012).
  • 9Sakamoto, M., Yabuta, K.: Boundedness of Marcinkiewicz functions. Studia Math., 135, 103-142 (1999).
  • 10Stein E. M.: Sigular Integral and Differentiability Properties of Functions, Princeton Univ. Press, Prince- ton, New Jersey, 1970.

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Acta Mathematica Sinica,English Series
2013年 第10期

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