This article is cited in 3 papers

BRIEF MESSAGE

Nikolskii–Bernstein constants in $L^{p}$ on the sphere with Dunkl weight

D. V. Gorbachev, N. N. Dobrovol'skii

Tula State University (Tula)

Abstract: We study the sharp Nikol'skii–Bernstein constants for spherical polynomials in the space $L^{p}(\mathbb{S}^{d})$ with the Dunkl weight. An interrelationship with one-dimensional constants for algebraic polynomials in the space $L^{p}[-1,1]$ with the Gegenbauer weight is established.

Keywords: Euclidean sphere, Dunkl weight, Gegenbauer weight, spherical polynomials, Nikolskii constant, Bernstein inequality.

UDC: 517.5

Received: 12.08.2020
Accepted: 22.10.2020

DOI: 10.22405/2226-8383-2018-21-4-302-307