On some improved weighted weak type inequalities

In this paper we obtain the sharp quantitative matrix weighted weak type bounds for the Christ–Goldberg maximal operator $M_{W,p}$ in the case $1<p<2$, improving a recent result by Cruz-Uribe and Sweeting. Also, in the scalar setting, we improve a weak type bound obtained in the aforementioned work for Calderón–Zygmund operators.