Corrigendum to ``Spherical Marcinkiewicz-Zygmund inequalities and positive quadrature''

Abstract

Professor Dr. Joachim Stockler has kindly pointed out to us that our proofs [2] of the estimates (4.5) and (4.9) are valid only in the case when we do not require the quadrature weights aξ to be nonnegative, since the Krein-Rutman extensions of nonnegative functionals are not guaranteed to be norm-preserving. The purpose of this note is to point out that the existence of nonnegative weights aξ satisfying (4.4) necessarily implies the following analogue (0.1) of (4.5). The existence of such weights was proved in the paper. (Here, and in the sequel, we use all the notation as in the paper.) ∥∥∥∥ aξ μq(Rξ) ∥∥∥∥ C,p′ ≤ c, 1 ≤ p′ ≤ ∞. (0.1)