On the Lebesgue constant for the Xu interpolation formula

In the paper [Y. Xu, Lagrange interpolation on Chebyshev points of two variables, J. Approx. Theory 87 (1996), 220-238], the author introduced a set of Chebyshev-like points for polynomial interpolation (by a certain subspace of polynomials) in the square [-1,1]^2 , and derived a compact form of the corresponding Lagrange interpolation formula. In [L. Bos, M. Caliari, S. De Marchi, M. Vianello, A numerical study of the Xu polynomial interpolation formula in two variables, Computing 76 (2006), 311-324], we gave an efficient implementation of the Xu interpolation formula and we studied numerically its Lebesgue constant, giving evidence that it grows like O((log n)^2 ), n being the degree. The aim of the present paper is to provide an analytic proof to show that the Lebesgue constant does have this order of growth.