Maciej Rzeszut

collaborators

5 papers

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.FA2025

Disjointification inequalities for Hoeffding subspaces of $H^{1}$ on an infinite polydisc

Maciej Rzeszut

We prove that the $L^{1}$ norm on the linear span of functions on $\T^\N$ dependent on $m$ variables and analytic and mean zero in each of them can be expressed as an interpolation s…

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…

math.FA2019

Weighted and multivariate Johnson--Schechtman inequalities with application to interpolation theory

Maciej Rzeszut

We prove a weighted version of a classical inequality of Johnson and Schechtman from which we derive a decomposition theorem for $p$ -th moments ( $0 < p \leq 1$ ) of nonnegative general…

One-sided Davis inequality for (F4) filtrations

Some remarks on Davis inequality for biparameter filtrations

Disjointification inequalities for Hoeffding subspaces of H1 on an infinite polydisc

Fefferman multiplier theorem for Hardy martingales

Weighted and multivariate Johnson--Schechtman inequalities with application to interpolation theory

Disjointification inequalities for Hoeffding subspaces of $H^{1}$ on an infinite polydisc