Agnieszka Hejna

activity

20182025

most citedHarmonic functions, conjugate harmonic functions and the Hardy space

H^{1}

in the rational Dunkl setting

7 citations · 8 across the 12 of their papers we have counts for

collaborators

Showing math.FAShow all

16 papers · 1 filter

math.FA2025

Littlewood-Paley square functions and the local Hardy space for Multi-Norm Structures on $R^{d}$

Agnieszka Hejna, Alexander Nagel, Fulvio Ricci

Multi-norm singular integrals and Fourier multipliers were introduced in [29], and one application of these notions was a precise description of the composition of convolution oper…

math.FA2025

Characterizations of $H^{1}$ and Fefferman-Stein decompositions of $BMO$ functions by systems of singular integrals in the Dunkl setting

Jacek Dziubański, Agnieszka Hejna

We extend the classical theorem of Uchiyama about constructive Fefferman-Stein decompositions of $BMO$ functions by systems of singular integrals to the rational Dunkl settin…

math.FA2024

On Lipschitz spaces in the Dunkl setting -- semigroup approach

Jacek Dziubański, Agnieszka Hejna

Let ${P_{t}}_{t > 0}$ be the Dunkl-Poisson semigroup associated with a root system $R \subset R^{N}$ and a multiplicity function $k \geq 0$ . Analogously to the classical theory,…

math.FA2023

A note on commutators of singular integrals with $BMO$ and $VMO$ functions in the Dunkl setting

Jacek Dziubański, Agnieszka Hejna

On $R^{N}$ equipped with a root system $R$ , multiplicity function $k \geq 0$ , and the associated measure $dw(\mathbf{x})=\prod_{α\in R}|\langle \mathbf{x},α\rangle|^{k(α)}\,d…

math.FA2022

Remarks on Dunkl translations of non-radial kernels

Jacek Dziubański, Agnieszka Hejna

On $R^{N}$ equipped with a root system $R$ and a multiplicity function $k > 0$ , we study the generalized (Dunkl) translations $τ_{x} g (- y)$ of not necessarily ra…

math.FA2022

On Dunkl Schrödinger semigroups with Green bounded potentials

Jacek Dziubański, Agnieszka Hejna

On $R^{N}$ equipped with a normalized root system $R$ , a multiplicity function $k (α) > 0$ , and the associated measure $$ dw(\mathbf x)=\prod_{α\in R}|\langle \mathbf x,α\rang…

math.FA2021

Upper and lower bounds for Dunkl heat kernel

Jacek Dziubański, Agnieszka Hejna

On $R^{N}$ equipped with a normalized root system $R$ , a multiplicity function $k (α) > 0$ , and the associated measure $$ dw(\mathbf x)=\prod_{α\in R}|\langle \mathbf x,α\rang…

math.FA2021

Dimension-free $L^{p}$ estimates for vectors of Riesz transforms in the rational Dunkl setting

Agnieszka Hejna

In this article, we prove dimension-free upper bound for the $L^{p}$ -norms of the vector of Riesz transforms in the rational Dunkl setting. Our main technique is Bellman function met…

math.FA2020★ 1 cited

Upper and lower bounds for Littlewood-Paley square functions in the Dunkl setting

Jacek Dziubański, Agnieszka Hejna

The aim of this paper is to prove upper and lower $L^{p}$ estimates, $1 < p < \infty$ , for Littlewood-Paley square functions in the rational Dunkl setting.

math.FA2019

Schrödinger operators with reverse Hölder class potentials in the Dunkl setting and their Hardy spaces

Agnieszka Hejna

For a normalized root system $R$ in $R^{N}$ and a multiplicity function $k \geq 0$ let $N = N + \sum_{α \in R} k (α)$ . Let $L = - Δ + V$ , $V \geq 0$ , be the Dunkl--Schrödinger ope…

math.FA2019

Singular integrals in the rational Dunkl setting

Jacek Dziubański, Agnieszka Hejna

On $R^{N}$ equipped with a normalized root system $R$ and a multiplicity function $k \geq 0$ let us consider a (non-radial) kernel $K (x)$ which has properties similar…

math.FA2019

On semigroups generated by sums of even powers of Dunkl operators

Jacek Dziubański, Agnieszka Hejna

On the Euclidean space $R^{N}$ equipped with a normalized root system $R$ , a multiplicity function $k \geq 0$ , and the associated measure $dw(\mathbf x)=\prod_{α\in R} |\langl…

math.FA2018

Hörmander's multiplier theorem for the Dunkl transform

Jacek Dziubański, Agnieszka Hejna

For a normalized root system $R$ in $R^{N}$ and a multiplicity function $k \geq 0$ let $N = N + \sum_{α \in R} k (α)$ . Denote by $dw(\mathbf x)=\prod_{α\in R}|\langle \mathb…

math.FA2018

Remark on atomic decompositions for Hardy space $H^{1}$ in the rational Dunkl setting

Jacek Dziubański, Agnieszka Hejna

Let $Δ$ be the Dunkl Laplacian on $R^{N}$ associated with a normalized root system $R$ and a multiplicity function $k (α) \geq 0$ . We say that a function $f$ belongs to the Har…

math.FA2018★ 7 cited

Harmonic functions, conjugate harmonic functions and the Hardy space $H^{1}$ in the rational Dunkl setting

Jean-Philippe Anker, Jacek Dziubański, Agnieszka Hejna

In this work we extend the theory of the classical Hardy space $H^{1}$ to the rational Dunkl setting. Specifically, let $Δ$ be the Dunkl Laplacian on a Euclidean space $R^{N}$ …

math.FA2018

Hardy spaces for the Dunkl harmonic oscillator

Agnieszka Hejna

Let $Δ$ and $L = Δ - ∥ x ∥^{2}$ be the Dunkl Laplacian and the Dunkl harmonic oscillator respectively. We define the Hardy space $H^{1}$ associated with the Dunkl harmonic…

Littlewood-Paley square functions and the local Hardy space for Multi-Norm Structures on Rd

Characterizations of H1 and Fefferman-Stein decompositions of BMO functions by systems of singular integrals in the Dunkl setting

On Lipschitz spaces in the Dunkl setting -- semigroup approach

A note on commutators of singular integrals with BMO and VMO functions in the Dunkl setting

Remarks on Dunkl translations of non-radial kernels

On Dunkl Schrödinger semigroups with Green bounded potentials

Upper and lower bounds for Dunkl heat kernel

Dimension-free Lp estimates for vectors of Riesz transforms in the rational Dunkl setting

Upper and lower bounds for Littlewood-Paley square functions in the Dunkl setting

Schrödinger operators with reverse Hölder class potentials in the Dunkl setting and their Hardy spaces

Singular integrals in the rational Dunkl setting

On semigroups generated by sums of even powers of Dunkl operators

Hörmander's multiplier theorem for the Dunkl transform

Remark on atomic decompositions for Hardy space H1 in the rational Dunkl setting

Harmonic functions, conjugate harmonic functions and the Hardy space H1 in the rational Dunkl setting

Hardy spaces for the Dunkl harmonic oscillator

Littlewood-Paley square functions and the local Hardy space for Multi-Norm Structures on $R^{d}$

Characterizations of $H^{1}$ and Fefferman-Stein decompositions of $BMO$ functions by systems of singular integrals in the Dunkl setting

A note on commutators of singular integrals with $BMO$ and $VMO$ functions in the Dunkl setting

Dimension-free $L^{p}$ estimates for vectors of Riesz transforms in the rational Dunkl setting

Remark on atomic decompositions for Hardy space $H^{1}$ in the rational Dunkl setting

Harmonic functions, conjugate harmonic functions and the Hardy space $H^{1}$ in the rational Dunkl setting