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Abstract

It is shown that maximal truncations of nonconvolution $L^2$-bounded singular integral operators with kernels satisfying Hörmander's condition are weak type $(1,1)$ and $L^p$-bounded for $1< p< \infty $. Under stronger smoothness conditions, such estimates can be obtained using a generalization of Cotlar's inequality. This inequality is not applicable here and the point of this article is to treat the boundedness of such maximal singular integral operators in an alternative way.