10 citations · 28 across the 12 of their papers we have counts for
15 papers
spaces in the Dunkl setting meet Coifman--Weiss--type atoms
Jacek Dziubański, Agnieszka Hejna-Łyżwa
Let be the Dunkl Laplacian associated with an arbitrary root system and a nonnegative multiplicity function. For every , a Coifman-Weiss type atomic characterizatio…
A note on commutators of singular integrals with and functions in the Dunkl setting
Jacek Dziubański, Agnieszka Hejna
On equipped with a root system , multiplicity function , and the associated measure $dw(\mathbf{x})=\prod_{α\in R}|\langle \mathbf{x},α\rangle|^{k(α)}\,d…
Remarks on Dunkl translations of non-radial kernels
Jacek Dziubański, Agnieszka Hejna
On equipped with a root system and a multiplicity function , we study the generalized (Dunkl) translations of not necessarily ra…
Harmonic functions, conjugate harmonic functions and the Hardy space in the rational Dunkl setting
Jean-Philippe Anker, Jacek Dziubański, Agnieszka Hejna
In this work we extend the theory of the classical Hardy space to the rational Dunkl setting. Specifically, let be the Dunkl Laplacian on a Euclidean space …
Sharp Gaussian estimates for heat kernels of Schrödinger operators
Krzysztof Bogdan, Jacek Dziubański, Karol Szczypkowski
We characterize functions for which the heat kernel of the Schrö\-dinger operator is comparable with the Gauss-Weierstrass kernel uniformly in space and time. In dim…
Hardy spaces for semigroups with Gaussian bounds
Jacek Dziubański, Marcin Preisner
Let T_t=e^{-tL} be a semigroup of self-adjoint linear operators acting on L^2(X,mu), where (X,d mu) is a space of homogeneous type. We assume that T_t has an integral kernel T_t(x,…
Strong continuity on Hardy spaces
Jacek Dziubański, Błażej Wróbel
We prove the strong continuity of spectral multiplier operators associated with dilations of certain functions on the general Hardy space introduced by Hofmann, Lu, Mitrea,…
Riesz transforms characterizations of Hardy spaces for the rational Dunkl setting and multidimensional Bessel operators
Jacek Dziubański
We characterize the Hardy space in the rational Dunkl setting associated with the reflection group by means of Riesz transforms. As a corollary we obtain a Ri…
A characterization of Hardy spaces associated with certain Schrödinger operators
Jacek Dziubański, Jacek Zienkiewicz
Let be the semigroup of linear operators generated by a Schrödinger operator on , , where satisfies $Δ^{-1} V\in L^\…
The Hardy space H1 in the rational Dunkl setting
Jean-Philippe Anker, Néjib Ben Salem, Jacek Dziubanski +1
This paper consists in a first study of the Hardy space H1 in the rational Dunkl setting. Following Uchiyama's approach, we characterizee H1 atomically and by means of the heat max…
Hardy spaces for Fourier--Bessel expansions
J. Dziubański, M. Preisner, L. Roncal +1
We study Hardy spaces for Fourier--Bessel expansions associated with Bessel operators on and . We define Hardy spaces as the sets of $L^…
Multivariate Hörmander-type multiplier theorem for the Hankel transform
Jacek Dziubański, Marcin Preisner, Błażej Wróbel
Let H(f)(x)=\int_{(0,infty)^d} f(v) E_{x}(v) dν(v), be the multivariable Hankel transform, where E_{x}(v)=\prod_{k=1}^d (x_k v_k)^{-a_k+1/2} J_{a_k-1/2}(x_k v_k), dν(v)=v^a dv, a=(…
On Riesz transforms characterization of H^1 spaces associated with some Schrödinger operators
Jacek Dziubański, Marcin Preisner
Let Lf(x)=-Δf(x) + V(x)f(x), V\geq 0, V\in L^1_{loc}(R^d), be a non-negative self-adjoint Schrödinger operator on R^d. We say that an L^1-function f belongs to the Hardy space H^1_…
Riesz transform characterization of Hardy spaces associated with Schrödinger operators with compactly supported potentials
Jacek Dziubański, Marcin Preisner
Let L=-Δ+V be a Schrödinger operator on R^d, d\geq 3. We assume that V is a nonnegative, compactly supported potential that belongs to L^p(R^d), for some p>d/2. Let K_t be the semi…
Distributions that are convolvable with generalized Poisson kernel of solvable extensions of homogeneous Lie groups
Ewa Damek, Jacek Dziubanski, Philippe Jaming +1
In this paper, we characterize the class of distributions on an homogeneous Lie group $\fN$ that can be extended via Poisson integration to a solvable one-dimensional extension $\f…