An observation on the Turán-Nazarov inequality (Q2856668)

\textit{F. L. Nazarov} [St. Petersbg. Math. J. 5, No. 4, 3--66 (1993); translation from Algebra Anal. 5, No. 4, 3--66 (1993; Zbl 0822.42001)] improved Turán's inequality and obtained an estimate for the maximum of the modulus of an exponential polynomial on an interval \(I\) in terms of the maximum of the modulus on a subset \(\Omega\) of the internal of positive Lebesgue measure. The estimate was given in terms of the Lebesgue measure of \(\Omega\) and the Lebesgue measure of \(I\).NEWLINENEWLINENEWLINEThe authors of the article under review show that in the Turán-Nazarov inequality the Lebesgue measure can be replaced by a certain geometric invariant.