Estimates for certain class of rough generalized Marcinkiewicz functions along submanifolds

Abstract

We establish certain delicate Lp{L}^{p} bounds for a class of generalized Marcinkiewicz integral operators along submanifolds with rough kernels. These bounds allow us to use Yano’s extrapolation method to prove the Lp{L}^{p} boundedness of the aforementioned integral operators under very weak assumptions on the kernels. Our results in this article improve and generalize many previously known results.

Keywords

• generalized marcinkiewicz
• triebel-lizorkin space
• rough kernels
• extrapolation
• 42b15
• 42b20
• 42b25
• 42b35