Let w exp(-Q), where Q is of faster than smooth polynomial growth at ~, for example, w k,α (x) exp(-exp k (|x| α )),α>1. We obtain a necessary and sufficient condition for mean convergence of Lagrange interpolation for such weights in L p (0<p=<1) completing earlier investigations by the first author and D.S. Lubinsky in L p (1<p<~).
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