Norm asymptotics of orthogonal polynomials for general measures

Letμ be a fixed positive unit Borel measure with infinite support in the unit disk. Acarrier of μ is any Borel subsetB of the support for whichμ(B)=1, and another such measurev iscarrier-related to μ when it has the same carriers asμ. Letp _n (z, v) be the monic orthogonal polynomial of degreen forv. We describe the possible asymptotics for the sequences {(∫|p _n (z,v)|² dv)1/2n} _n≥1 which are associated to the set of measures carrier-related to μ.