 Capacity of a bounded set thickened by a symplectic subspace

If $U$ is nonempty, bounded and open in standard symplectic Euclidean space, and $W$ is a codimension-two symplectic subspace, a linear symplectic change of coordinates makes $W=\{q_1=p_1=0\}$. Boundedness of the remaining coordinate projection places $U+W$ inside a finite-radius symplectic cylinder. Openness puts a small ball inside it. Monotonicity and normalization of a symplectic capacity give the displayed strict bounds.