  In this paper we study a question related to the continuity of maximal
operators of convolution type acting on $W^{1,1}(\mathbb{R})$. We prove that
the map $u\mapsto (u^{*})'$ is continuous from $W^{1,1}(\mathbb{R})$ to
$L^{1}(\mathbb{R})$, where $u^{*}$ is the maximal function associated to the
Poisson kernel, the Heat kernel or a family of kernels related to the
fractional Laplacian. This is the first result of this type for a centered
maximal operator.
