  In the Drury-Arveson space, we consider the subspace of functions whose
Taylor coefficients are supported in the complement of a set
$Y\subset\mathbb{N}^d$ with the property that $Y+e_j\subset Y$ for all
$j=1,\dots,d$. This is an easy example of shift-invariant subspace, which can
be considered as a RKHS in is own right, with a kernel that can be explicitely
calculated. Moreover, every such a space can be seen as an intersection of
kernels of Hankel operators, whose symbols can be explicity calcuated as well.
Finally, this is the right space on which Drury's inequality can be optimally
adapted to a sub-family of the commuting and contractive operators originally
considered by Drury.
