Weak type L1 boundedness of CZOs with odd rough kernels

For f∈S(Rd) and Ω∈L1(Sd−1),∫Sd−1Ω(x′)dx′=0, the singular integral operator TΩ is defined byTΩ(f)(x)=limε→0+⁡∫|x−y|≥εΩ(y/|y|)|y|df(x−y)dy. In this paper, we prove some sufficient conditions for odd Ω∈H1 such that TΩ is weak type L1-bounded.