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In this work, we establish L^p₁ L^p₁ Lᵖ bounds for maximal multi- (sub) linear singular integrals associated with homogeneous kernels ({y') }|{y|^mn} where is an Lq function on the unit sphere S^mn-1 with vanishing moment condition and q>1. As an application, we obtain almost everywhere convergence results for the associated doubly truncated multilinear singular integrals.
Bae Jun Park (Sat,) studied this question.
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