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A Martingale Study of the Beurling–Ahlfors Transform inRn [PDF]

Journal of Functional Analysis, 1997
We apply the theory of martingale transforms to study the Beurling–Ahlfors transform,S, in dimensionsn⩾2. This operator reveals a rich structure through its representation as a martingale, and we obtain new results concerning the operator norm ofSacting ...
Rodrigo Bañuelos
exaly   +2 more sources

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Optimal estimates for martingale transforms

Journal of Functional Analysis, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jinghao Huang, Fedor Sukochev, Dmitriy Zanin   +2 more
openaire   +1 more source

A martingale transformation for superprocesses

Statistics & Probability Letters, 2012
This note deals with a new martingale transformation for superprocesses with general branching mechanisms (including discontinuous processes and processes with non-local branchings). It consists of three sections. In the first one, the authors start by defining superprocesses and the branching mechanism.
He, Hui, Luan, Nana
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Martingale transforms and weak Orlicz–Hardy spaces of predictable martingales

Statistics & Probability Letters, 2014
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Yu, Lin, Yin, Huan
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LOGARITHMIC GROWTH FOR MATRIX MARTINGALE TRANSFORMS

Journal of the London Mathematical Society, 2001
An example is given of an operator weight W that satisfies the dyadic operator Hunt–Muckenhoupt–Wheeden condition [Aopf ]d2 for which there exists a dyadic martingale transform on L2 (W) that is unbounded. The construction relates weighted boundedness to the boundedness of dyadic vector Hankel operators.
Gillespie, T. A., Pott, S., Treil, S., Volberg, A.   +3 more
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Maximal Inequalities of Noncommutative Martingale Transforms

Canadian Journal of Mathematics, 2019
AbstractIn this paper, we investigate noncommutative symmetric and asymmetric maximal inequalities associated with martingale transforms and fractional integrals. Our proofs depend on some recent advances on algebraic atomic decomposition and the noncommutative Gundy decomposition. We also prove several fractional maximal inequalities.
Jiao, Yong, Sukochev, Fedor, Zhou, Dejian   +2 more
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Martingale transforms and fractional integrals on rearrangement-invariant martingale Hardy spaces

Periodica Mathematica Hungarica, 2020
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Two-Dimensional Conjugate Martingale Transforms

Acta Mathematica Hungarica, 2000
The author derives several characterizations of the two-dimensional Hardy space \(H_1\) as well as of BMO- and VMO-martingale spaces generated by bounded Vilenkin systems via conjugate martingale transforms.
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Martingale transforms and Hardy spaces

Probability Theory and Related Fields, 1992
Burkholder's martingale transforms are especially useful in studying ``predictable'' martingale Hardy spaces. ``Characterizations'' of such spaces via martingale transforms are provided.
Chao, J.-A., Long, R.-L.
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A Sharp Inequality for Martingale Transforms

2011
If d= (d 1, d 2, …) is a martingale difference sequence and e1e2,… are numbers in {– 1, 1}, then $$P\left( {|\sum \nolimits ^n_{k = 1^{\varepsilon_k}}\,{{d_k}}| \geq \lambda } \right) \leq c||\sum \nolimits ^n_{k = 1}\,{d_k} |{|_1}$$ (1) where c is some absolute constant.
Burgess Davis, Renming Song
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