In this paper we establish that the maximal operator and the Littlewood-Paley
g-function associated with the heat semigroup defined by multidimensional
Bessel operators are of weak type (1,1). Also, we prove that Riesz transforms
in the multidimensional Bessel setting are of strong type (p,p), for every
$1<p<\infty$, and of weak type (1,1).