On rough generalized Marcinkiewicz integrals along surfaces of revolution on product spaces

Abstract

In this paper, we prove the $ L^p $ boundedness of generalized Marcinkiewicz operators along surfaces of revolution on product spaces under very weak conditions on the the singular kernels. Our results generalize and improve many previously known results.

Keywords

• singular kernels
• marcinkiewicz integrals
• generalized marcinkiewicz
• product domains
• surfaces of revolution