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L^p Boundedness for Parabolic Littlewood-Paley Operators with Rough Kernels Belonging to Block Spaces 被引量：1

L^p Boundedness for Parabolic Littlewood-Paley Operators with Rough Kernels Belonging to Block Spaces
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摘要 This paper is primarily concerned with the proof of the Lp boundedness of parabolic Littlewood-Paley operators with kernels belonging to certain block spaces. Some known results are essentially extended and improved. This paper is primarily concerned with the proof of the Lp boundedness of parabolic Littlewood-Paley operators with kernels belonging to certain block spaces. Some known results are essentially extended and improved.
作者 Dong Xiang CHEN Shan Zhen LU
机构地区 School of Mathematics School of Mathematics
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2010年第2期277-286,共10页 数学学报（英文版）
基金 Supported by National Natural Science Foundation of China (Grant Nos. 10961015, 10871173) National Natural Science Foundation of Jiangxi Province (2008GZS0051) the doctor foundation of Jiangxi Normal University (2443)
关键词 parabolic Littlewood-Paley operator Fourier transform rough kernel block space parabolic Littlewood-Paley operator, Fourier transform, rough kernel, block space
分类号 O178 [理学—基础数学] O177.3 [理学—基础数学]
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参考文献9

  • 1Fabes, E., Rivire, N.: Singular integrals with mixed homogeneity. Studia Math., 27, 19-38 (1966).
  • 2Madych, W. R.: On Littlewood-Paley functions. Studia Math., 50, 43-63 (1974).
  • 3Ding, Y., Xue, Q., Yabuta, K.: Parabolic Littlewood Paley g-function with rough kernel. Acta Mathematica Sinica, English Series, 24, 2049-2060 (2008).
  • 4Lu, S., Taibleson, M., Weiss, G.: Spaces Generated by Blocks, Beijing Normal Univ. Press, Beijing, 1989.
  • 5Keitoku, M., Sato, E.: Block spaces on the unit sphere in R^n. Proc. Amer. Math. Soc., 119, 453-455 (1993).
  • 6Chen, Y., Ding, Y.: A parabolic singular integral operator with rough kernel. J. Australian Math. Soc., 84, 163 -179 (2008).
  • 7Al-Qassem, H. M., Al-Salman, A. J.: A note on Marcinkiewicz integral operators. J. Math. Anal. Appl., 282, 698-710 (2003).
  • 8Ricci, F., Stein, E. M.: Multiparameter Singular integrals and maximal functions. Ann. Inst. Fourier, 42, 637-670 (1992).
  • 9Rubio de Francial, J. L.: Maximal function and fourier transforms. Duke Math. J., 53, 395-403 (1986).

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Acta Mathematica Sinica,English Series
2010年 第2期

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