非齐次粗糙核参数型Marcinkiewicz算子的Hp有界性

陶祥兴, 张松艳

数学学报 ›› 2011, Vol. 54 ›› Issue (1) : 97-110.

PDF(560 KB)
中国科学院数学与系统科学研究院期刊网
PDF(560 KB)
数学学报 ›› 2011, Vol. 54 ›› Issue (1) : 97-110. DOI: 10.12386/A2011sxxb0011
论文

非齐次粗糙核参数型Marcinkiewicz算子的Hp有界性

    陶祥兴1, 张松艳2
作者信息 +

Hp Bounds for Parametric Marcinkiewicz Operators with Nonhomogenous Rough Kernels

    Xiang Xing TAO1, Song Yan ZHANG2
Author information +
文章历史 +

摘要

设Ω是球面上函数, b是径向函数, ρ是实部正的复数;设Ψ为C2([0,∞))的递增凸函数, Ψ(0) = 0.本文研究非齐次粗糙核参数型Marcinkiewicz算子μρΩ,b,以及旋转曲面上的非齐次粗糙核参数型Marcinkiewicz算子μρΩ,Ψ,b, 给出非齐次粗糙核Ω和b的最小光滑性条件,建立算子μρΩ,b和μρΩ, Ψ,b在Hardy空间和弱Hardy空间上的有界性.本文结果推进了先前b≡1情形的已有工作.

 

Abstract

Let Ω be a function on the unit sphere and b a radial function, and ρ be a complex parameter with Re (ρ)>0. Let Ψ be in C2([0,∞)), convex, and increasing function with Ψ(0) = 0. The parametric Marcinkiewicz operator μρΩ, b with nonhomogenous rough kernel and the rough Marcinkiewicz operator μρΩ, Ψ, b related to a surface of revolutions are considered in this paper, we prove the boundedness of these Marcinkiewicz operators on Hardy spaces and weak Hardy spaces under the minimum smooth conditions for the rough kernels Ω and b. The results in this paper extend as well as improve previously known results.

 

关键词

参数型Marcinkiewicz算子 / 径向核及粗糙核 / Hardy空间及弱Hardy空间

Key words

Parametric Marcinkiewicz operator / radial kernel and rough kernel / Hardy space and weak Hardy space

引用本文

EndNote

Ris (Procite)

Bibtex

导出引用
陶祥兴, 张松艳. 非齐次粗糙核参数型Marcinkiewicz算子的Hp有界性. 数学学报, 2011, 54(1): 97-110 https://doi.org/10.12386/A2011sxxb0011
Xiang Xing TAO, Song Yan ZHANG. Hp Bounds for Parametric Marcinkiewicz Operators with Nonhomogenous Rough Kernels. Acta Mathematica Sinica, Chinese Series, 2011, 54(1): 97-110 https://doi.org/10.12386/A2011sxxb0011

参考文献


[1] Stein E. M., On the function of Littlewood--Paley, lusin and marcinkiewicz, Trans. Amer. Math. Soc., 1958, 88: 430--466.

[2] H\"ormander L., Translation invariant operators, Acta. Math., 1960, 104, 93--139.

[3] Ding Y., Lu S. Z., Yabuta K., A problem on rough parametric Marcinkiewicz functions, J. Austral. Math. Soc., 2002, 72: 13--21.

[4] AL-Salman A., AL-Qassem H., On the Lp boundedness of rough parametric Marcinkiewicz functions, J. Ineq. Pure Appl. Math., 2007, 8(4): 108--115.

[5] Ding Y., Lu S. Z., Xue Q. Y., Marcinkiewicz integral on Hardy spaces, Integr. Equ. Oper. Theory, 2002, 42: 174--182.

[6] Lin C. C., Lin Y. C., Hpw-Lpw Boundedness of Marcinkiewicz integral, Integr. Equ. Oper. Theory, 2007, 58: 87--98.

[7] Zhang S. Y., Tao X. X., Rough parametric Marcinkiewicz integrals on generalized Camoanato spaces, Acta Math. Scientia, 2010, 30A(1): 154--166.

[8] Al-Qassem H., Lp estimates for rough parametric Marcinkiewicz integrals, SUT J. Math., 2004, 40(2): 117--131.

[9] Tao X. X., Wei R. Y., Boundedness of commutators related to Marcinkiewicz integrals with variable kernels in Herz-type Hardy spaces, Acta Math. Scientia, 2009, 29A(6): 1508--1517.

[10] Lin C. C., Lin Y. C., Tao X. X., Yu X., The boundedness of Marcinkiewicz integral with variable kernel, Illinois J. Math., 2009, 53(1): 197--217.

[11] Fefferman R., Soria F., The weak Hardy space H1, Studia Math., 1987, 85: 1--16.

[12] Liu H. P., The weak Hp space on homogeneous groups, Lecture Notes in Math., 1991, 1494: 113--118.

基金

国家自然科学基金资助项目(10771110);宁波市自然科学基金资助项目(2009A610084)

PDF(560 KB)

328

Accesses

0

Citation

Detail
段落导航
相关文章

/

〈 〉