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

Let 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<∞).