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A Remark on Hörmander Multipliers on Dunkl Hardy Spaces
Abstract
Let ℛ be a normalized root system in ℝN with a nonnegative multiplicity function k, and let ℱ be the associated Dunkl transform. We prove a Hörmander multiplier theorem on the Hardy spaces HpDunkl, 0<p≤1, defined by conical Littlewood--Paley square functions. Let W2s denote the classical Sobolev space in ℝN. More precisely, if a multiplier m satisfies supt>0 |ψ(·)m(t·)|W2s<∞ for a nonzero radial cutoff ψ∈ Cc∞(ℝN∖{0}) and s>N(1/p−1/2), where N is the homogeneous dimension, then the Dunkl multiplier 𝒯mf=ℱ−1(mℱf) extends to a bounded operator on HpDunkl.
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BibTeX
@misc{dziubanski2026remark,
title = {{A Remark on Hörmander Multipliers on Dunkl Hardy Spaces}},
author = {Jacek Dziubański and Agnieszka Hejna-Łyżwa},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18621},
eprint = {2609.18621},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18621},
}
RIS
TY - UNPB
TI - A Remark on Hörmander Multipliers on Dunkl Hardy Spaces
AU - Jacek Dziubański
AU - Agnieszka Hejna-Łyżwa
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.18621
UR - https://arxiv.org/abs/2609.18621
AB - Let ℛ be a normalized root system in ℝ^N with a nonnegative multiplicity function k, and let ℱ be the associated Dunkl transform. We prove a Hörmander multiplier theorem on the Hardy spaces H^p_Dunkl, 0<p≤1, defined by conical Littlewood--Paley square functions. Let W_2^s denote the classical Sobolev space in ℝ^N. More precisely, if a multiplier m satisfies sup_t>0 |ψ(·)m(t·)|_W_2^s<∞ for a nonzero radial cutoff ψ∈ C_c^∞(ℝ^N∖{0}) and s>N(1/p−1/2), where N is the homogeneous dimension, then the Dunkl multiplier 𝒯_mf=ℱ^−1(mℱf) extends to a bounded operator on H^p_Dunkl.
ER -