A weak-type inequality for uniformly bounded trigonometric polynomials

Autor:	E. D. Livshits
Rok vydání:	2013
Předmět:	Discrete mathematics Combinatorics Mathematics (miscellaneous) Operator (physics) Bernstein inequalities Uniform boundedness Order (ring theory) Trigonometry Trigonometric polynomial Constant (mathematics) Action (physics) Mathematics
Zdroj:	Proceedings of the Steklov Institute of Mathematics. 280:208-219
ISSN:	1531-8605 0081-5438
DOI:	10.1134/s0081543813010148
Popis:	This paper is devoted to refining the Bernstein inequality. Let D be the differentiation operator. The action of the operator Λ = D/n on the set of trigonometric polynomials Tn is studied: the best constant is sought in the inequality between the measures of the sets {x ∈ T: |Λt(x)| > 1} and {x ∈ T: |t(x)| > 1}. We obtain an upper estimate that is order sharp on the set of uniformly bounded trigonometric polynomials TnC = {t ∈ Tn: ‖t‖ ≤ C}.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::9477870bf885ea0424cc0b553001c85f https://doi.org/10.1134/s0081543813010148 Zobrazit plný text záznamu Full text from SpringerLink