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

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.