On Certain Estimates for Parabolic Marcinkiewicz Integrals Related to Surfaces of Revolution on Product Spaces and Extrapolation

Abstract

In this paper, appropriate Lp bounds for particular classes of parabolic Marcinkiewicz integrals along surfaces of revolution on product spaces are obtained. These bounds allow us to use Yano’s extrapolation argument to obtain the Lp boundedness of the aforesaid integral operators under weak conditions on the kernels. These conditions on the kernels are the best possible among their respective classes. In this work, several previously known results on Marcinkiewicz integrals are fundamentally improved and extended.

Keywords

• extrapolation
• rough parabolic integrals
• surfaces of revolution
• product spaces