A note on mean convergence of Lagrange interpolation in Lp(0<p⩽1)

AbstractLet w≔exp(−Q), where Q is of faster than smooth polynomial growth at ∞, for example, wk,α(x)≔exp(−expk(|x|α)),α>1. We obtain a necessary and sufficient condition for mean convergence of Lagrange interpolation for such weights in Lp(0<p⩽1) completing earlier investigations by the first author and D.S. Lubinsky in Lp(1<p<∞)