Marcinkiewicz积分L^p的有界性

L^p Boundedness for the Marcinkiewicz Integral

本文研究Marcinkiewicz积分算子 μΩ 的Lp(Rn)有界性 ,证明了当核函数Ω∈L(logL) 1 2(Sn- 1 )时 ,μΩ 是L2 (Rn)有界的 ;Ω∈L(logL)β(Sn- 1 ) ( 12 <β <1 )时 ,μΩ 是Lp(Rn) ( 1 /β <p <1 /( 1 - β) )有界的。

The higher dimensional Marcinkiewicz integral introduced by Stein is considered. Some conditions implying the L 2(R n) and the L p(R n) boundedness for the Marcinkiewicz integral are obtained.