The purpose of this paper is to study the validity of the Paley inequality on square function, for noncommutative martingales. Let {Mathematical expression} be a regular gage space, and {Mathematical expression} a sequence of von-Neumann algebras such that {Mathematical expression} we prove that for every {Mathematical expression}, where e{open}n(F) is the conditional expectation of F with respect to the subalgebra {Mathematical expression}: We also consider the case of a martingale arising in the context of harmonic analysis on noncommutative discrete groups, in analogy to the theorem of R.E.A.C. Paley on Fourier-Walsh series. © 1978 Fondazione Annali di Matematica Pura ed Applicata.
Alesina, A., DE MICHELE, L. (1978). Inequalities of Paley type for noncommutative martingales. ANNALI DI MATEMATICA PURA ED APPLICATA, 116(1), 143-150 [10.1007/BF02413871].
Inequalities of Paley type for noncommutative martingales
DE MICHELE, LEONEDE
1978
Abstract
The purpose of this paper is to study the validity of the Paley inequality on square function, for noncommutative martingales. Let {Mathematical expression} be a regular gage space, and {Mathematical expression} a sequence of von-Neumann algebras such that {Mathematical expression} we prove that for every {Mathematical expression}, where e{open}n(F) is the conditional expectation of F with respect to the subalgebra {Mathematical expression}: We also consider the case of a martingale arising in the context of harmonic analysis on noncommutative discrete groups, in analogy to the theorem of R.E.A.C. Paley on Fourier-Walsh series. © 1978 Fondazione Annali di Matematica Pura ed Applicata.
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