‎in this paper‎, ‎we study the $l^p$ ($1

‎In this paper‎, ‎we study the $L^p$ ($1

We prove Lp estimates of a class generalized Marcinkiewicz integral operators with mixed homogeneity on product domains. By using these along an extrapolation argument, we obtain the boundedness our under very weak conditions kernel functions. Our results in this paper improve and extend several known both integrals parabolic

*Correspondence: [email protected] Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid, Jordan Abstract In this article, we establish Lp estimates for parametric Marcinkiewicz integral operators with rough kernels. These estimates and extrapolation arguments improve and extend some known results on Marcinkiewicz integrals. MSC: Primary 40B20; secondary 4...

A multilinear version of the Boyd interpolation theorem is proved in the context of quasi-normed rearrangement-invariant spaces. A multilinear Marcinkiewicz interpolation theorem is obtained as a corollary. Several applications are given, including estimates for bilinear fractional integrals.

In this paper, we show a Marcinkiewicz type interpolation theorem for Orlicz spaces. As an application, obtain existence result parabolic equation in divergence form.

In this paper, we establish certain Lp bounds for several classes of rough Marcinkiewicz integrals over surfaces revolution on product spaces. By using these and an extrapolation argument, obtain the boundedness under very weak conditions kernel functions. Our results represent natural extensions improvements known integrals.