一类Marcinkiewicz积分算子的双权有界性

TWO-WEIGHTED BOUNDEDNESS FOR A CLASS OF MARCINKIEWICZ INTEGRAL OPERATORS

本文研究了Marcinkiewicz积分μΩ的有界性的问题,借助Ap权的性质,得到了相应与Littlewood-Paley g-函数的Marcinkiewica积分算子μΩ的(Lp(v),Lp(u))有界性,并且证明了相应于Littlewood-Paley gλ*-函数和Lusin面积积分的Marcinkiewicz积分μ*Ω,λ,μΩ,S的(Lp(v),Lp(u))有界性.

In this paper, the boundedness for a class of Marcinkiewiez Integrals is considered. Following the properties of Ap weight, we give the （L^p （υ） ,L^p （u）） boundedness for Marcinkiewicz integral operator μα related to the Littlewood-Paley g-function. Moreover, the （L^p （υ）,L^p （u）） boundedness for Marcinkiewicz integral operators μα,λ^＊, and μα,s related to the Littlewood-Paley gλ-function and the Lusin area integral S is obtained.