ON ROUGH GENERALIZED PARAMETRIC MARCINKIEWICZ INTEGRALS

被引：17
|
作者：
Al-Qassem, H. [1 ]
Cheng, L. [2 ]
Pan, Y. [3 ]
机构：
[1] Qatar Univ, Dept Math & Phys, Doha, Qatar
[2] Bryn Mawr Coll, Dept Math, Bryn Mawr, PA 19010 USA
[3] Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA
来源：
JOURNAL OF MATHEMATICAL INEQUALITIES | 2017年 / 11卷 / 03期
关键词：
Marcinkiewicz integrals; Triebel-Lizorkin spaces; rough kernels; Orlicz spaces; Block spaces; extrapolation; L-p boundedness; SINGULAR-INTEGRALS; OPERATORS; BOUNDEDNESS; SPACES;
D O I：
10.7153/jmi-2017-11-60
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We obtain certain sharp L-p bounds for the generalized parametric Marcinkiewicz integrals M-Omega,h,rho((lambda)). The singular kernels are allowed to be rough on the unit sphere as well as in the radial direction. By the virtue of these estimates along with an extrapolation argument we obtain some new and improved results on generalized parametric Marcinkiewicz integrals. Our conditions on O and h are known to be the weakest conditions in their respective classes. One of our main results answers a question posed by Fan and Wu.
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页码：763 / 780
页数：18
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