Non-commutative Stein inequality and its applications

Mohammad Sal Moslehian and Ali Talebi

Communications in Statistics - Theory and Methods, 2019, vol. 48, issue 7, 1611-1620

Abstract: The non-commutative Stein inequality asks whether there exists a constant Cp, q depending only on p, q such that ∑n|En(xn)|q1qp≤Cp,q∑n|xn|q1qp(Sp,q),\begin{equation*} \left\Vert \left(\sum _{n} |\mathcal {E}_{n} (x_n) |^{q}\right)^{\frac{1}{q}} \right\Vert _p \le C_{p,q} \left\Vert \left(\sum _{n} | x_n |^q \right)^{\frac{1}{q}}\right\Vert _p\qquad \qquad (S_{p,q}), \end{equation*} for all (positive) sequences (xn) in Lp(M)$L_p(\mathcal {M})$. The validity of (Sp, 2) for 1

Date: 2019
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DOI: 10.1080/03610926.2018.1435813

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