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...
متن کاملMartingale Transforms and Related Singular
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...
متن کاملOn Singular Integral and Martingale Transforms
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...
متن کاملOn the unboundedness of martingale transforms
© Springer-Verlag, Berlin Heidelberg New York, 1985, tous droits réservés. L’accès aux archives du séminaire de probabilités (Strasbourg) (http://portail. mathdoc.fr/SemProba/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impressio...
متن کاملTesting Conditional Independence using Conditional Martingale Transforms
This paper investigates testing conditional independence between Y and Z given λθ(X) for some θ ∈ Θ ⊂ R, for a function λθ(·) known upto a parameter θ ∈ Θ. First, the paper proposes a new method of conditional martingale transforms under which tests are asymptotically pivotal and asymptotically unbiased against √ n-converging Pitman local alternatives. Second, the paper performs an analysis of ...
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ژورنال
عنوان ژورنال: The Annals of Mathematical Statistics
سال: 1966
ISSN: 0003-4851
DOI: 10.1214/aoms/1177699141