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Lp estimates for Dunkl--Schrödinger operators
Abstract
We study the Dunkl--Schrödinger operator L=−Δk+V on ℝN, N>2, where V is a nonnegative potential in the reverse Hölder class RHq(dw), q>N/2, and N is the homogeneous dimension. We establish decay estimates for the resolvent kernel in terms of the critical radius and the orbit distance. For reflection-invariant potentials, we obtain Lp(dw) bounds for VL−1, second-order Dunkl derivatives of L−1, and the Riesz transform ∇kL−1/2, together with fractional potential and mixed estimates. The proofs combine local estimates for weak solutions, the Dunkl Fefferman--Phong inequality, and kernel estimates adapted to the Euclidean and orbit distances.
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BibTeX
@misc{hejnalyzwa2026estimates,
title = {{$L^p$ estimates for Dunkl--Schrödinger operators}},
author = {Agnieszka Hejna-Łyżwa and Suman Mukherjee},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.08371},
eprint = {2610.08371},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.08371},
}
RIS
TY - UNPB
TI - L^p estimates for Dunkl--Schrödinger operators
AU - Agnieszka Hejna-Łyżwa
AU - Suman Mukherjee
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.08371
UR - https://arxiv.org/abs/2610.08371
AB - We study the Dunkl--Schrödinger operator L=−Δ_k+V on ℝ^N, N>2, where V is a nonnegative potential in the reverse Hölder class RH^q(dw), q>N/2, and N is the homogeneous dimension. We establish decay estimates for the resolvent kernel in terms of the critical radius and the orbit distance. For reflection-invariant potentials, we obtain L^p(dw) bounds for VL^−1, second-order Dunkl derivatives of L^−1, and the Riesz transform ∇_kL^−1/2, together with fractional potential and mixed estimates. The proofs combine local estimates for weak solutions, the Dunkl Fefferman--Phong inequality, and kernel estimates adapted to the Euclidean and orbit distances.
ER -