ABSTRACT
The non-commutative Stein inequality asks whether there exists a constant Cp, q depending only on p, q such that
for all (positive) sequences (xn) in
. The validity of (Sp, 2) for 1 < p < ∞ and (Sp, 1) for 1 ⩽ p < ∞ are known. In this paper, we verify (i) (Sp, ∞) for 1 < p ⩽ ∞; (ii) (Sp, p) for 1 ⩽ p < ∞; (iii) (Sp, q) for 1 ⩽ q ⩽ 2 and q < p < ∞. We also present some applications.
MATHEMATICS SUBJECT CLASSIFICATION:
Acknowledgments
The second author was supported by a grant from Ferdowsi University of Mashhad (No. 2/45592).