Generalized Marcinkiewicz Operators Aassociated to Twisted Surfaces

Mohammed Ali1,2,∗

1College of Integrative Studies, Abdullah Al-Salem University, Khaldiya, Kuwait

2Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid, Jordan

Email: mohammed.ali@aasu.edu.kw

Abstract

This paper is concerned with studying the mapping properties of generalized Marcinkiewicz integral operators

along twisted surfaces. Under certain conditions on the􀀀s esurfaces weobtain certain Lp estimates for these

operators provided that the kernel functions are in Lq Sn−1 × Sm−1 . By an extrapolation argument, we

prove that these operators are bounded on Lp(Rn × Rm) for 1 < p < ∞ under very weak conditions on the

kernel functions. Our results extend and improve many previously known results.

Keywords: Generalized Marcinkiewicz operator; Twisted surfaces; Rough kernels