Finite-dimensional subspaces of Lp with Lipschitz metric projection

Resumo

We prove that the metric projection onto a finite-dimensional subspace Y ⊂ L_p, p ∈ (1, 2) ∪ (2, ∞), satisfies the Lipschitz condition if and only if every function in Y is supported on finitely many atoms. We estimate the Lipschitz constant of such a projection for the case in which the subspace is one-dimensional.