Abstract
In this paper, the authors study the mapping properties of singular integrals on product domains with kernels in L(log + L) ɛ( S m-1× S n-1)(ɛ=1 or 2) supported by hyper-surfaces. The L p bounds for such singular integral operators as well as the related Marcinkiewicz integral operators are established, provided that the lower dimensional maximal function is bounded on L q( R 3) for all q>1. The condition on the integral kernels is known to be optimal.
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