A note on weak type L1 boundedness of CZOs with rough kernels ✩

For f ∈ S(R2) and Ω ∈ L1(S1), S1 Ω(x )dx = 0, define TΩ(f )(x) = lim →0+ |x−y| Ω(y/|y|) |y|2 f (x −y)dy. In this paper, we shall prove that there is a class of functions in H1(S1) −Lln+ L(S1) such that TΩ is weak type L1-bounded. © 2007 Elsevier Inc. All rights reserved.