Weak type bounds for rough maximal singular integrals near $L^1$

Ankit Bhojak, Parasar Mohanty

In this paper it is shown that for $\Omega \in L\log L({\mathbb{S}}^{d-1})$, the rough maximal singular integral operator $T_{\Omega }^{\ast }$ is of weak type $L\log \log L({\mathbb{R}}^d)$. Furthermore,…