Maciej Rzeszut

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math.PR2025

One-sided Davis inequality for (F4) filtrations

Maciej Rzeszut

The classical Davis inequality $E M f ≃ E S f$ , where $(S f)^{2} = \sum_{k} ∣ f_{k} - f_{k - 1} ∣^{2}$ is the square function and $M f = sup_{n} ∣ f_{n} ∣$ is…

math.PR2025

Some remarks on Davis inequality for biparameter filtrations

Maciej Rzeszut

The Davis inequality $E S f ≃ E f^{*}$ between $L^{1}$ norms of square function of a martingale and its maximal function is known for martingales indexed by linear…

math.PR2025

Fefferman multiplier theorem for Hardy martingales

Maciej Rzeszut

A well-known theorem due to Fefferman provides a characterization of Fourier multipliers from $H^{1} (T)$ to $ℓ^{1}$ , i.e. sequences $(λ_{n})_{n = 0}^{\infty}$ such tha…