Jensen's inequality for polynomials with concentration at low degrees (Q1078705)

Let \(p(x)=a_ 0+a_ 1x+a_ 2x^ 2+...\), be a polynomial with complex coefficients. Let \(0<d<1\). Then p(x) is said to have concentration d at degrees at most k, if (*) \(\sum^{j=k}_{j=0}| a_ j| \geq d\sum | a_ j|\). The aim of the paper under review is to extend Jensen's inequality for polynomials normalized by \(\sum | a_ j| =1\) and satisfying condition (*).