Lagrange interpolation at Pollaczek--Laguerre zeros on the real semiaxis

In order to approximate functions defined on the real semiaxis, which can grow exponentially both at $0$ and at $+infty$, we introduce a suitable Lagrange operator based on the zeros of orthogonal polynomials with respect to the weight $w(x)=x^gamma mathrm{e}^{-x^{-alpha}-x^eta}$. We prove that this interpolation process has Lebesgue constant with order $log(m)$ in weighted uniform metric and converges with the order of the best approximation in a large subset of weighted $L^p-$spaces, $p in (1,infty)$