A Singular Riesz Product in the Nevai Class and Inner Functions with the Schur Parameters in ∩p>2 lp Original Research Article

There exist singular Riesz products dσ=∏∞κ=1 (1+Re(ακζnκ)) on the unit circle T with the parameters (an)n⩾0 of orthogonal polynomials in L2(dσ) satisfying ∑∞n=0 |an|p<+∞ for every p, p>2. The Schur parameters of the inner factor of the Cauchy integral ∫T (ζ−z)−1 dσ(ζ), σ being such a Riesz product, belong to ∩p>2 lp.