期刊文献+

粗糙核带参数的抛物型Marcinkiewicz函数的一个注记 被引量:1

A note on parametric parabolic Marcinkiewicz functions with rough kernels
下载PDF
导出
摘要 主要研究了带参数的抛物型Marcinkiewicz函数μσΩ,h(f)的L2(Rn)有界性,用核的分解技术和Fourier变换估计的方法分别在当1<γ<∞,h∈Hγ(R+),Ω∈L(log L)1/γ(SnΩ1)条件下和当1<γ≤∞,h∈Ωγ(R+),Ω∈Llog+L(SnΩ1)条件下,建立了μσΩ,h(f)的L2(Rn)有界性,并推广了以前学者的结论. This note is concerned with L^2(R^n) boundedness of parametric parabolic Marcinkiewicz function μσΩ,h(f). Under the conditions 1〈-γ〈∞,h∈Hγ'(IR)+),Ω∈L(logL)1/γ(Sn-1)) and 1〈γ≤∞,h∈△γ((IR)+),Ω∈Llog+L(Sn-1), using kernel decomposition technique and Fourier transform estimate, the L^(Rn) boundedness is obtained for μσΩ,h(f) respectively. The well-known results by before scholars are extended.
出处 《纯粹数学与应用数学》 CSCD 2010年第5期735-744,共10页 Pure and Applied Mathematics
基金 国家自然科学基金(10571014 10671158)
关键词 MARCINKIEWICZ积分 带参数的抛物型Marcinkiewicz函数 粗糙核 Marcinkiewiez integral, parametric parabolic Marcinkiewicz function, rough kernel
  • 相关文献

参考文献2

二级参考文献13

  • 1徐靖南,朱维申,白世伟.压剪应力作用下多裂隙岩体的力学特性——本构模型[J].岩土力学,1993,14(4):1-15. 被引量:22
  • 2Calderon, A. P., Torchinsky, A.: Parabolic maximal functions associated with a distribution. Adv. Math., 16, 1-64 (1975)
  • 3Fabes, E. B., Riviere, N. M.: Singular integrals with mixed homogeneity. Studia Math., 27, 19-38 (1966)
  • 4Hofmann, S.: A characterization of commutators of parabolic singular integrals, Fourier anaiysis and partial differential equations (Miraflores de la Siera, 1992), Stud. Adv. Math. CRC, Boca Raton, FL 1995, 195-210
  • 5Hofmann, S.: Parabolic singular integrals of Calderon-type, rough operators, and caloric layer potentials. Duke Math. J., 90(2), 209-259 (1997)
  • 6Tao, T.: The weak-type (1,1) of LlogL homogeneous convolution operators. Indiana U. Math. J., 48, 1547-1584 (1999)
  • 7Stein, E. M.: On the functions of Littlewood-Paley, Lusin and Marcinkiewicz. Trans. Amer. Math. Soc., 88, 430-466 (1958)
  • 8Ding, Y., Fan, D., Pan, Y.: LP-boundedness of Marcinkiewicz integrals with Hardy space function kernel. Acta Mathematica Sinica, English Series, 16(4), 593-600 (2000)
  • 9Madych, W. R.: On Littlewood-Paley functions. Studia Math., 50, 43-63 (1974)
  • 10Hormander, L.: Estimates for translation invariant operators in L^p spaces. Acta Math. 104, 93-140 (1960)

共引文献93

同被引文献6

引证文献1

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部