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Riesz transform characterization of Hardy spaces associated with Dunkl--Schrödinger operators
Abstract
Let L=−Δk+V be a Schrödinger operator associated with the Dunkl Laplacian and a nonnegative potential. We characterize the Hardy space HL1, defined by the maximal operator of the semigroup generated by −L, in terms of the Riesz transforms associated with L. Under a local integral condition on the potential and a decay condition on the semigroup, formulated relative to an admissible covering by cubes, we prove that |f|HL1 asymp |f|L1(dw) +∑j=1N |R̃j f|L1(dw). The proof combines an atomic characterization of HL1 with local Hardy space theory and weighted integral estimates for Dunkl derivatives of the heat kernels. The result applies to arbitrary root systems and nonnegative multiplicity functions.
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BibTeX
@misc{hejnalyzwa2026riesz,
title = {{Riesz transform characterization of Hardy spaces associated with Dunkl--Schrödinger operators}},
author = {Agnieszka Hejna-Łyżwa},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.00703},
eprint = {2610.00703},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.00703},
}
RIS
TY - UNPB
TI - Riesz transform characterization of Hardy spaces associated with Dunkl--Schrödinger operators
AU - Agnieszka Hejna-Łyżwa
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.00703
UR - https://arxiv.org/abs/2610.00703
AB - Let L=−Δ_k+V be a Schrödinger operator associated with the Dunkl Laplacian and a nonnegative potential. We characterize the Hardy space H_L^1, defined by the maximal operator of the semigroup generated by −L, in terms of the Riesz transforms associated with L. Under a local integral condition on the potential and a decay condition on the semigroup, formulated relative to an admissible covering by cubes, we prove that |f|_H_L^1 asymp |f|_L^1(dw) +∑_j=1^N |R̃_j f|_L^1(dw). The proof combines an atomic characterization of H_L^1 with local Hardy space theory and weighted integral estimates for Dunkl derivatives of the heat kernels. The result applies to arbitrary root systems and nonnegative multiplicity functions.
ER -