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Marcinkiewicz-Zygmund inequalities for hemispherical $t$-designs
In this paper, we introduce a new set of $\mathbb{L}_2$-orthogonal polynomials on the hemisphere $\mathbb{S}^d_+:=\{\mathbf{x}\in\mathbb{R}^{d+1}:\|\mathbf{x}\|=1, \mathbf{x}\cdot\mathbf{e}_{d+1}\geq0\}$ and establish $\mathbb{L}_1$ Marcinkiewicz-Zygmund inequalities on the hemisphere for even and o
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