BMO and commutators of martingale transforms

Svante Janson

Displaying similar documents to “BMO and commutators of martingale transforms”

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Rodrigo Bañuelos (1987)

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Walter Schachermayer (1996)

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Eiichi Nakai (1997)

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Let E and F be spaces of real- or complex-valued functions defined on a set X. A real- or complex-valued function g defined on X is called a pointwise multiplier from E to F if the pointwise product fg belongs to F for each f ∈ E. We denote by PWM(E,F) the set of all pointwise multipliers from E to F. Let X be a space of homogeneous type in the sense of Coifman-Weiss. For 1 ≤ p < ∞ and for $ϕ : X \times ℝ_{+} \to ℝ_{+}$ , we denote by $b m o_{ϕ, p} (X)$ the set of all functions $f \in L_{l o c}^{p} (X)$ such that $s u p_{a \in X, r > 0} 1 / ϕ (a, r) (1 / μ (B (a, r)) ʃ_{B (a, r)} | f (x) - f_{B (a, r)} {|^{p} d μ)}^{1 / p} < \infty$ , where B(a,r) is the ball centered...

A remark on a problem of Girsanov

Norihiko Kazamaki (1978)

Séminaire de probabilités de Strasbourg

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Nicolas Th. Varopoulos (1981)

Annales de l'institut Fourier

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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 $m$ .

A remark on the class of martingales with bounded quadratic variation

Norihiko Kazamaki (1989)

Séminaire de probabilités de Strasbourg

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