Asymptotic estimates of holomorphic sections on Bohr-Sommerfeld Lagrangian submanifolds

Let M be a complex manifold and L be a line bundle over M with a Hermitian metric h whose Chern form is a Kähler form ω. Let X ⊂ M be a compact Lagrangian submanifold of (M, ω). When X satisfies the Bohr-Sommerfeld condition, we give an asymptotic estimate of the norm |f|hᵏ on X for f ∈ H⁰(M, Lᵏ).