Marcinkiewicz-Zygmund inequalities for hemispherical $t$-designs

Chao Li, Xiaojun Chen

In this paper, we introduce a new set of ${\mathbb{L}}_2$-orthogonal polynomials on the hemisphere $\mathbb{S}^d_+:=\{\mathbf{x}\in\mathbb{R}^{d+1}:\|\mathbf{x}\|=1, \mathbf{x}\cdot\…