On the influence of the geometric properties of the spectrum of a polynomial on the Nikol'skij inequalities of different metrics

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) Inequalities for sums, series and integrals (26D15) Inequalities for trigonometric functions and polynomials (26D05) Trigonometric polynomials, inequalities, extremal problems (42A05)