Nikol’skii’s inequality of different metrics for trigonometric polynomials in a space with mixed asymmetric norm
НЕРАВЕНСТВО РАЗНЫХ МЕТРИК НИКОЛЬСКОГО ДЛЯ ТРИГОНОМЕТРИЧЕСКИХ ПОЛИНОМОВ В ПРОСТРАНСТВЕ СО СМЕШАННОЙ НЕСИММЕТРИЧНОЙ НОРМОЙ
Akishev G.
2023Krasovskii Institute of Mathematics and Mechanics
Trudy Instituta Matematiki i Mekhaniki UrO RAN
2023#29Issue 411 - 26 pp.
A Lebesgue space of 2π-periodic functions of m variables with a mixed norm is considered. Based on this Lebesgue space, a space with a mixed asymmetric norm is defined. The main aim of the paper is to prove Nikol’skii’s inequality of different metrics for multiple trigonometric polynomials in spaces with mixed asymmetric norms. The paper consists of an introduction and three sections. In the first section, several auxiliary statements about the asymmetric norm of a multiple trigonometric polynomial are proved. In the second section, Nikol’skii’s inequality of different metrics is proved for multiple trigonometric polynomials in spaces with mixed asymmetric norms. In the third section, the accuracy of Nikol’skii’s inequality for multiple trigonometric polynomials is established. An extremal polynomial is constructed.
Nikol’skii’s inequality of different metrics , space with asymmetric norm , trigonometric polynomial
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Lomonosov Moscow University, Kazakhstan Branch, Astana, 100001, Kazakhstan
Institute of Mathematics and Mathematical Modeling, Kazakhstan
Lomonosov Moscow University
Institute of Mathematics and Mathematical Modeling
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