Hardy-Littlewood-Sobolev inequality in Lorentz spaces

The Young inequality in Lorentz spaces covers these cases: if $p_1,p_2,p\in]1,\infty[$, $q_1,q_2,q\in[1,\infty]$, \begin{equation} \|f\ast g\|_{L^{p,q}}\leq C\|f\|_{L^{p_1,q_1}} \|g\|_{L^{p_2,q_2}},\qquad p_1^{-1}+p_2^{-1} =1+p^{-1},\ q_1^{-1}+q_2^{-1}\geq q^{-1}; \end{equation} and if $p_{1},p_2\in ]1,\infty[$, $q_1,q_2\in[1,\infty]$, then \begin{equation} \|f\ast g\|_{L^\infty}\leq C\|f\|_{L^{p_1,q_1}} \|g\|_{L^{p_2,q_2}},\qquad p_1^{-1}+p_2^{-1} =1,\ q_1^{-1}+q_2^{-1}\geq1. \end{equation} Note that the second inequality contains your estimate.

The oldest reference I know for this is a paper by R.O'Neil, Convolution operators and $L(p,q)$ spaces, Duke Math. J. 30 (1963), 129-142.