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Displaying similar documents to “A theorem on weak type estimates for Riesz transforms and martingale transforms”

Conjugate martingale transforms

Ferenc Weisz (1992)

Studia Mathematica

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Characterizations of H₁, BMO and VMO martingale spaces generated by bounded Vilenkin systems via conjugate martingale transforms are studied.

BMO and commutators of martingale transforms

Svante Janson (1981)

Annales de l'institut Fourier

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The commutator of multiplication by a function and a martingale transform of a certain type is a bounded operator on L p , 1 < p < , if and only if the function belongs to BMO. This is a martingale version of a result by Coifman, Rochberg and Weiss.

Martingale operators and Hardy spaces generated by them

Ferenc Weisz (1995)

Studia Mathematica

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Martingale Hardy spaces and BMO spaces generated by an operator T are investigated. An atomic decomposition of the space H p T is given if the operator T is predictable. We generalize the John-Nirenberg theorem, namely, we prove that the B M O q spaces generated by an operator T are all equivalent. The sharp operator is also considered and it is verified that the L p norm of the sharp operator is equivalent to the H p T norm. The interpolation spaces between the Hardy and BMO spaces are identified by...

Carthaginian enlargement of filtrations

Giorgia Callegaro, Monique Jeanblanc, Behnaz Zargari (2013)

ESAIM: Probability and Statistics

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This work is concerned with the theory of initial and progressive enlargements of a reference filtration 𝔽 F with a random time. We provide, under an equivalence assumption, slightly stronger than the absolute continuity assumption of Jacod, alternative proofs to results concerning canonical decomposition of an 𝔽 F -martingale in the enlarged filtrations. Also, we address martingales’ characterization in the enlarged filtrations in terms of martingales in the reference filtration, as...

Harmonic interpolating sequences, L p and BMO

John B. Garnett (1978)

Annales de l'institut Fourier

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Let ( z ν ) be a sequence in the upper half plane. If 1 < p and if y ν 1 / p f ( z ν ) = a ν , ν = 1 , 2 , ... ( * ) has solution f ( z ) in the class of Poisson integrals of L p functions for any sequence ( a ν ) p , then we show that ( z ν ) is an interpolating sequence for H . If f ( z ν ) = a ν , ν = 1 , 2 , ... has solution in the class of Poisson integrals of BMO functions whenever ( a ν ) , then ( z ν ) is again an interpolating sequence for H . A somewhat more general theorem is also proved and a counterexample for the case p 1 is described.

An almost-sure estimate for the mean of generalized Q -multiplicative functions of modulus 1

Jean-Loup Mauclaire (2000)

Journal de théorie des nombres de Bordeaux

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Let Q = ( Q k ) k 0 , Q 0 = 1 , Q k + 1 = q k Q k , q k 2 , be a Cantor scale, 𝐙 Q the compact projective limit group of the groups 𝐙 / Q k 𝐙 , identified to 0 j k - 1 𝐙 / q j 𝐙 , and let μ be its normalized Haar measure. To an element x = { a 0 , a 1 , a 2 , } , 0 a k q k + 1 - 1 , of 𝐙 Q we associate the sequence of integral valued random variables x k = 0 j k a j Q j . The main result of this article is that, given a complex 𝐐 -multiplicative function g of modulus 1 , we have lim x k x ( 1 x k n x k - 1 g ( n ) - 0 j k 1 q j 0 a q j g ( a Q j ) ) = 0 μ -a.e .

On a weak type (1,1) inequality for a maximal conjugate function

Nakhlé Asmar, Stephen Montgomery-Smith (1997)

Studia Mathematica

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In their celebrated paper [3], Burkholder, Gundy, and Silverstein used Brownian motion to derive a maximal function characterization of H p spaces for 0 < p < ∞. In the present paper, we show that the methods in [3] extend to higher dimensions and yield a dimension-free weak type (1,1) estimate for a conjugate function on the N-dimensional torus.

A martingale approach to general Franklin systems

Anna Kamont, Paul F. X. Müller (2006)

Studia Mathematica

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We prove unconditionality of general Franklin systems in L p ( X ) , where X is a UMD space and where the general Franklin system corresponds to a quasi-dyadic, weakly regular sequence of knots.

Riesz transforms for the Dunkl Ornstein-Uhlenbeck operator

Adam Nowak, Luz Roncal, Krzysztof Stempak (2010)

Colloquium Mathematicae

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We propose a definition of Riesz transforms associated to the Ornstein-Uhlenbeck operator based on the Dunkl Laplacian. In the case related to the group ℤ ₂ it is proved that the Riesz transform is bounded on the corresponding L p spaces, 1 < p < ∞.