Asymptotic behavior inside the disk for Lebesgue Sobolev orthogonal polynomials (Q701403)

The behavior inside and on the unit disk, for monic orthogonal polynomials with respect to the following Sobolev inner product \[ \langle f,g\rangle_s= \int^{2\pi}_0 f(e^{i\sigma})\overline{g(e^{i\sigma})} d\mu(\sigma)+ \int^{2\pi}_0 f'(e^{i\sigma})\overline{g'(e^{i\sigma}} {d\sigma\over 2\pi}, \] where \(d\mu(\sigma)\) is a finite Borel measure on \([0,2\pi]\) with infinite support and \({d\sigma\over 2\pi}\) is the normalized Lebesgue measure, is studied. The aim of the paper is to study when the symptotic formula can be extended up to the boundary and inside the disk.