Abstract :
In this paper we offer a new approach to C. de Boor′s conjecture of the L∞-boundedness of the L2-projector PS onto the spline space Sm−1(Δn). This approach is based on the strengthening of the "exponential decay" property of the fundamental spline. It is proved, first, that the Lp-norm of the operator PS is uniformly bounded without any restrictions on the mesh Δn at least in some neighbourhood of p = 2 and, second, that the Lp-norm of the operator PS for all p ∈ [1, ∞] is uniformly bounded in meshes Δn with a fixed number of nodes n.
