Abstract
Abstract We establish certain delicate L p {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 L p {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.
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