Resumen de On Bernstein type quantitative estimates for Ornstein non-inequalities

Krystian Kazaniecki, Michal Wojciechowski

• For the sequence of multi-indices {αj}j=1m and β, we study the inequality ∥Dβf∥L1(Td)≤KNj=1∑m∥Dαjf∥L1(Td), where f is a trigonometric polynomial of degree at most N on the d-dimensional torus. Assuming some natural geometric property of the set {αj}∪{β}, we show that KN≥C(lnN)ϕ, where ϕ<1 depends only on the set {αj}∪{β}.