Singular integral operators with non-smooth kernels on irregular domains

Let ? be a space of homogeneous type. The aims of this paper are as follows. i) Assuming that T is a bounded linear operator on L2(?), we give a sufficient condition on the kernel of T such that T is of weak type (1,1), hence bounded on Lp(?) for 1 0 |Teu(x)|, to be Lp bounded, 1 < p < 8. Applications include weak (1,1) estimates of certain Riesz transforms, and Lp boundedness of holomorphic functional calculi of linear elliptic operators on irregular domains