A generalization of Jensen’s inequality for polynomials having concentration at low degrees

In this paper we give some asymptotic estimates for the best lower bound C(d,k,p)C(d,k,p) of the Jensen’s functional J(f)=∫02πlog|f(eiθ)|dθ2π for when the polynomial ff has a concentration dd at low degrees kk measured by the lplp-norm under the LpLp-norm, p>2p>2.