International Journal of Mathematics and Mathematical Sciences
Volume 27 (2001), Issue 8, Pages 495-503
doi:10.1155/S0161171201006548
Rough Marcinkiewics integral operators
Hussain Al-Qassem
and Ahmad Al-Salman
Department of Mathematics, Yarmouk University, Irbid, Jordan
Abstract
We study the Marcinkiewicz integral operator M𝒫f(x)=(∫−∞∞|∫|y|≤2tf(x−𝒫(y))(Ω(y)/|y|n−1)dy|2dt/22t)1/2, where 𝒫 is a polynomial mapping from ℝn into ℝd and Ω is a homogeneous function of degree zero on ℝn with mean value zero over the unit sphere Sn−1. We prove an Lp boundedness result of M𝒫 for rough Ω.