Asymptotics of Sobolev orthogonal polynomials on the unit ball

Sobolev orthogonal polynomials on the unit ball are studied. The corresponding Sobolev inner product is defined involving outward normal derivatives on the sphere. We will give explicit representation for orthogonal polynomials and reproducing kernels in term of classical polynomials on the ball. From these explicit expressions, algebraic properties and asymptotic behaviour of Christoffel functions will be deduced.