On Bernstein type quantitative estimates for Ornstein non-inequalities
Krystian Kazaniecki
Johannes Kepler University Linz, Austria; University of Warsaw, PolandMichal Wojciechowski
Polish Academy of Sciences, Warsaw, Poland
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Abstract
For the sequence of multi-indices and , we study the inequality
where is a trigonometric polynomial of degree at most on the -dimensional torus. Assuming some natural geometric property of the set , we show that
where depends only on the set .
Cite this article
Krystian Kazaniecki, Michal Wojciechowski, On Bernstein type quantitative estimates for Ornstein non-inequalities. Rev. Mat. Iberoam. 40 (2024), no. 3, pp. 901–912
DOI 10.4171/RMI/1441