$L^\infty$ boundedness of density for free additive convolutions
Résumé
We show that the density of the free additive convolution of two Borel probability measures $\mu,\nu$ on $\mathbb R$ whose Cauchy transforms have reasonably good behaviour at infinity is bounded whenever $\mu(\{a\})+\nu(\{b\})<1$ for all $a,b\in\mathbb R$.