International Journal of Mathematics and Mathematical Sciences
Volume 27 (2001), Issue 8, Pages 495-503

Rough Marcinkiewicz integral operators

Hussain Al-Qassem and Ahmad Al-Salman

Department of Mathematics, Yarmouk University, Irbid, Jordan

Received 16 January 2001

Copyright © 2001 Hussain Al-Qassem and Ahmad Al-Salman. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We study the Marcinkiewicz integral operator M𝒫f(x)=(||y|2tf(x𝒫(y))(Ω(y)/|y|n1)dy|2dt/22t)1/2, where 𝒫 is a polynomial mapping from n into d and Ω is a homogeneous function of degree zero on n with mean value zero over the unit sphere Sn1. We prove an Lp boundedness result of M𝒫 for rough Ω.