On Bernstein type quantitative estimates for Ornstein non-inequalities

• Krystian Kazaniecki ^[2] ; Michal Wojciechowski ^[1]
  1. [1] Polish Academy of Sciences

     Polish Academy of Sciences

     Warszawa, Polonia

     
  2. [2] Johannes Kepler University Linz, Austria; University of Warsaw, Poland
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 40, Nº 3, 2024, págs. 901-912
• Idioma: inglés
• DOI: 10.4171/RMI/1441
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• Resumen

  • 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}.