A note on martingale transforms and $A_{p}$-weights

Rodrigo Bañuelos

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Conjugate martingale transforms

Ferenc Weisz (1992)

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

On the class LlogL, martingales, and singular integrals

Richard Gundy (1969)

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A theorem on weak type estimates for Riesz transforms and martingale transforms

Nicolas Th. Varopoulos (1981)

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The Riesz transforms of a positive singular measure $ν \in M (R^{n})$ satisfy the weak type inequality $m [\sum_{j = 1}^{n} | R_{j} ν | > λ] \geq \frac{C ∥ ν ∥}{λ}, λ > 0$ where $m$ denotes Lebesgue measure and $C$ is a positive constant only depending on $m$ .

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 $L^{p}$ , $1 < p < \infty$ , 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)

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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...

Schatten classes and commutators on simple martingales

J. Chao, Lizhong Peng (1996)

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Attainable claims with p'th moments

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On compact Ito's formulas for martingales of m .

María Jolis (1990)

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We prove that the class m of continuous martingales with parameter set [0,1], bounded in L, is included in the class of semi-martingales S (L(P)) defined by Allain in [A]. As a consequence we obtain a compact Itô's formula. Finally we relate this result with the compact Itô formula obtained by Sanz in [S] for martingales of m .

Displaying similar documents to “A note on martingale transforms and A p -weights”

Displaying similar documents to “A note on martingale transforms and $A_{p}$ -weights”