A note on mean convergence of Lagrange interpolation in L-p (0 < p <= 1)

Abstract

Let w:= exp(-Q), where Q is of faster than smooth polynomial growth at infinity, for example, w(k,x)(x):= exp(-exp(k)(/x/(x))), alpha > 1. We obtain a necessary and sufficient condition for mean convergence of Lagrange interpolation for such weights in L-p (0 < p less than or equal to 1) completing earlier investigations by the first author and D.S. Lubinsky in L-p (1 < p < infinity). (C) 2001 Elsevier Science B.V. All rights reserved.