Coisotropic Ekeland–Hofer capacities

For subsets in the standard symplectic space $(\mathbb{R}^{2n},\omega_0)$ whose closures are intersecting with coisotropic subspace $\mathbb{R}^{n,k}$ we construct relative versions of Ekeland-Hofer capacities respect to $\mathbb{R}^{n,k}$, establish representation formulas for such bounded convex domains $\mathbb{R}^{n,k}$. We also prove a product formula and fact that value this capacity on hypersurface $\mathcal{S}$ restricted contact type containing origin is equal action generalized leafwise chord $\mathcal{S}$.