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) of the Jensen's functional J(f)[email protected]!"0^2^@plog|f(e^i^@q)|[email protected]@p for when the polynomial f has a concentration d at low degrees k measured by the l"p-norm under the L"p-norm, p>2.