$L^1$-Dini conditions and limiting behavior of weak type estimates for singular integrals

Yong Ding, Xudong Lai

In 2006, Janakiraman [10] showed that if $\Omega$ with mean value zero on $S^{n-1}$ satisfies the condition \[ \sup_{|ξ|=1}\int_{S^{n-1}}|Ω(θ)-Ω(θ+δξ)|dσ(θ)\leq Cnδ\int_{S^{n-1}}|Ω(θ)|d…