Restricted weak type on maximal linear and multilinear integral maps

It is shown that multilinear operators of the form $T(f_1,...,f_k)(x)$ $=\int_{\mathbb{R}^n}K(x,y_1,...,y_k)f_1(y_1)... f_k(y_k)dy_1...dy_k$ of restricted weak type $(1,...,1,q)$ are always of weak type $(1,...,1,q)$ whenever the map $x\to K_x$ is a locally integrable $L^1(\mathbb{R}^n)$-valued function.