Orthogonal polynomials for weights close to indeterminacy

We obtain estimates for Christoffel functions and orthogonal polynomials for even weights W:R→[0,∞) that are ‘close’ to indeterminate weights. Our main example is exp(-|x|(log|x|)β), with β real, possibly modified near 0, but our results also apply to exp(-|x|α(log|x|)β),α<1. These types of weights exhibit interesting properties largely because they are either indeterminate or are close to the border between determinacy and indeterminacy in the classical moment problem.