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

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