Publications

My research interests focus on various aspects of real harmonic analysis, in particular:

singular integrals and Paley–Littlewood theory in different contexts, such as discrete singular integrals, multiparameter singular integrals related to multi-norm structures, Dunkl-type singular integrals, the Hilbert transform, and Riesz transforms;
structures of function spaces and their norms, including Hardy spaces (one- and multi-parameter), BMO and VMO spaces, Lipschitz (Hölder) spaces, oscillation and variation norms;
semigroups of linear operators and their associated generators and operators, such as Schrödinger operators with various potentials, Riesz and Bessel potentials;
analytic aspects of Dunkl theory, including the Dunkl heat kernel, the Dunkl convolution and translation, and the dependence of estimates on the underlying reflection group and multiplicity function.

Reseach papers

Dziubański, Jacek and Hejna, Agnieszka. "A note on commutators of singular integrals with BMO and VMO functions in the Dunkl setting." Math. Nachr., 2024. DOI: 10.1002/mana.202300106.
Dziubański, Jacek and Hejna, Agnieszka. "Remarks on Dunkl translations of non-radial kernels." J. Fourier Anal. Appl., 2023. DOI: 10.1007/s00041-023-10034-2.
Dziubański, Jacek and Hejna, Agnieszka. "Upper and lower bounds for the Dunkl heat kernel." Calc. Var. Partial Differential Equations, 2023. DOI: 10.1007/s00526-022-02370-w.
Hejna, Agnieszka. "Dimension-free Lp-estimates for vectors of Riesz transforms in the rational Dunkl setting." J. Anal. Math., 2023. DOI: 10.1007/s11854-023-0278-z.
Dziubański, Jacek and Hejna, Agnieszka. "Singular integrals in the rational Dunkl setting." Rev. Mat. Complut., 2022. DOI: 10.1007/s13163-021-00402-1.
Dziubański, Jacek and Hejna, Agnieszka. "Upper and lower bounds for Littlewood-Paley square functions in the Dunkl setting." Studia Math., 2022. DOI: 10.4064/sm200716-16-4.
Hejna, Agnieszka. "Behavior of eigenvalues of certain Schrödinger operators in the rational Dunkl setting." Analysis and Mathematical Physics, 2021. DOI: 10.1007/s13324-021-00556-7.
Hejna, Agnieszka. "Schrödinger operators with reverse Hölder class potentials in the Dunkl setting and their Hardy spaces." J. Fourier Anal. Appl., 2021. DOI: 10.1007/s00041-021-09841-2.
Dziubański, Jacek and Hejna, Agnieszka. "On semigroups generated by sums of even powers of Dunkl operators." Integral Equations and Operator Theory, 2021. DOI: 10.1007/s00020-021-02646-4.
Anker, Jean-Philippe and Dziubański, Jacek and Hejna, Agnieszka. "Harmonic functions, conjugate harmonic functions and the Hardy space H1 in the rational Dunkl setting." J. Fourier Anal. Appl., 2019. DOI: 10.1007/s00041-019-09666-0.
Dziubański, Jacek and Hejna, Agnieszka. "Hörmander's multiplier theorem for the Dunkl transform." J. Funct. Anal., 2019. DOI: 10.1016/j.jfa.2019.03.002.
Hejna, Agnieszka. "Hardy spaces for the Dunkl harmonic oscillator." Math. Nachr., 2020. DOI: 10.1002/mana.201900215.
Dziubański, Jacek and Hejna, Agnieszka. "Remark on atomic decompositions for the Hardy space H1 in the rational Dunkl setting." Studia Math., 2020. DOI: 10.4064/sm180618-25-11.
Dziubański, Jacek and Hejna, Agnieszka. "Remarks on localized sharp functions on certain sets in Rn." Monatsh. Math., 2018. DOI: 10.1007/s00605-017-1091-5.

Articles accepted for publications

Dziubański, Jacek and Hejna, Agnieszka. "On Dunkl-Schrödinger semigroups with Green bounded potentials." Praca przyjęta do druku w Constructive Approximation, 2025. DOI: 10.48550/ARXIV.2204.03443.

Preprints

Dziubański, Jacek and Hejna, Agnieszka. "On Lipschitz spaces in the Dunkl setting -- semigroup approach." 2024. arXiv:2408.12399.
Dziubański, Jacek and Hejna, Agnieszka. "Characterizations of H1 and Fefferman-Stein decompositions of BMO functions by systems of singular integrals in the Dunkl setting." 2025. arXiv:2503.04964.

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