Orthogonal polynomials on the circle for the weight w satisfying   conditions: w,1/w in BMO(T)
  In the case when the weight and its inverse belong to BMO(T), we prove the asymptotics of the monic orthogonal polynomials in L^p, 2<p<p_0. Immediate applications include the estimates on the uniform norm and asymptotics for the polynomial entropy. 
S. Denisov, K. Rush
math.CA