Marcinkiewicz-Zygmund and interpolating families on the ball

This paper examines points and weights on the unit ball $\mathbb{B}^{d}$ that satisfy $L_{p}$ , $0< p\le \infty $ , Marcinkiewicz-Zygmund inequalities and interpolating inequalities with respect to a doubling weight. We show some permutational results of these families and provide necessary density conditions for spaces of polynomials in terms of the Beuring-Landau density. These conditions are also sharp, which can be attained by the Fekete arrays on $\mathbb{B}^{d}$ .