منابع مشابه
Non - Commutative Martingale Transforms
We prove that non-commutative martingale transforms are of weak type (1, 1). More precisely, there is an absolute constant C such that if M is a semi-finite von Neumann algebra and (Mn)n=1 is an increasing filtration of von Neumann subalgebras of M then for any non-commutative martingale x = (xn) ∞ n=1 in L 1(M), adapted to (Mn)n=1, and any sequence of signs (εn) ∞ n=1, ∥∥∥∥ε1x1 + N ∑ n=2 εn(xn...
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We prove the analogue of the classical Burkholder-Gundy inequalites for noncommutative martingales. As applications we give a characterization for an Ito-Clifford integral to be an L-martingale via its integrand, and then extend the Ito-Clifford integral theory in L, developed by Barnett, Streater and Wilde, to L for all 1 < p < ∞. We include an appendix on the non-commutative analogue of the c...
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The operators obtained by taking conditional expectation of continuous time martingale transforms are studied, both on the circle T and on R". Using a Burkholder-Gundy inequality for vector-valued martingales, it is shown that the vector formed by any number of these operators is bounded on LP(R"), 1 < p < oo, with constants that depend only on p and the norms of the matrices involved. As a cor...
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Linear equivalences of norms of vector-valued singular integral operators and vector-valued martingale transforms are studied. In particular, it is shown that the UMD-constant of a Banach space X equals the norm of the real (or the imaginary) part of the BeurlingAhlfors singular integral operator, acting on LpX(R ) with p ∈ (1,∞). Moreover, replacing equality by a linear equivalence, this is fo...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2002
ISSN: 0022-1236
DOI: 10.1006/jfan.2002.3952