  We derive a dyadic model operator for the Riesz vector. We show linear upper
$L^p$ bounds for $1 < p < \infty$ between this model operator and the Riesz
vector, when applied to functions with values in Banach spaces. By an upper
bound we mean that the boundedness of the dyadic Riesz vector implies the
boundedness of the Riesz vector. The same holds for single dyadic Riesz
transforms and their continuous counterparts. The linear dependence is with
constant one.
