On certain estimates for Marcinkiewicz integrals and extrapolation

被引：0
作者：
Hussain Al-Qassem
Yibiao Pan
机构：
[1] Qatar University,Department of Mathematics and Physics
[2] University of Pittsburgh,Department of Mathematics
来源：
Collectanea mathematica | 2009年 / 60卷
关键词：
Marcinkiewicz integrals; maximal functions; boundedness; rough kernel; block spaces; extrapolation; Primary 42B20; Secondary 42B15; 42B25;
D O I：
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学科分类号：
摘要：
We obtainLp estimates for parametric Marcinkiewicz integrals associated to polynomial mappings and with rough kernels on the unit sphere as well as on the radial direction. These estimates will allow us to use an extrapolation argument to obtain some new and improved results on Marcinkiewicz integrals. Also, such estimates provide us with a unifying approach in dealing with Marcinkiewicz integrals when the kernel function ω belongs to the class of block spacesB q(0,α) (Sn-1) as well as when ω belongs to the classL(logL)α (Sn-1). Our conditions on the kernels are known to be the best possible in their respective classes.
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页码：123 / 145
页数：22
相关论文
共 32 条
  • [1] Al-Qassem H.M.(2003)A note on Marcinkiewicz integral operators J. Math. Anal. Appl. 282 698-710
  • [2] Al-Salman A.J.(2002) estimates for singular integrals with kernels belonging to certain block spaces Rev. Mat. Iberoamericana 18 701-730
  • [3] Al-Qassem H.M.(2002) bounds for the function of Marcinkiewicz Math. Res. Lett. 9 697-700
  • [4] Pan Y.(2002)Singular integrals with rough kernels in J. London Math. Soc. 66 153-174
  • [5] Al-Salman A.J.(1977) log Bull. Amer. Math. Soc. 83 569-645
  • [6] Al-Qassem H.M.(2002)( Michigan Math. J. 50 17-26
  • [7] Cheng L.C.(2002)) J. Aust. Math. Soc. 72 13-21
  • [8] Pan Y.(1986)Extensions of Hardy spaces and their use in analysis Invent. Math. 84 541-561
  • [9] Al-Salman A.J.(1997)On the Amer. J. Math. 119 799-839
  • [10] Pan Y.(1960) boundedness of Marcinkiewicz integrals Acta Math. 104 93-140
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