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Weak type (1,1) and strong type {p,p) inequalities are proved for operators defined by oscillating kernels. The techniques are sufficiently general to derive versions of these inequalities using weighted norms. 0. Introduction. Given a positive real number a > 0, a ^ 1, define the oscillating kernel Ka by Ka(x) = (l + \x\)-1eW and consider the convolution… (More)

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