BMO-Type characterizations and endpoint estimates for commutators of intrinsic square functions on Orlicz-Hardy spaces
Abstract
The commutators of intrinsic square functions associated with the intrinsic Littlewood--Paley g-function, the intrinsic gλ*-function and the intrinsic Lusin area function can be used to characterize BMO-type function spaces through their boundedness properties. In this paper, we show that, for b∈ BMO(ℝn), the boundedness of each of these commutators from the Musielak--Orlicz Hardy space Hφ(ℝn) to Lφ(ℝn) is equivalent to b∈ BMOφ(ℝn) (a nontrivial subspace of BMO(ℝn)), under suitable assumptions on the growth function φ. This extends the weighted characterization of Han and Wu [Proc. Amer. Math. Soc. 152(1) (2024), 281--293] to the Musielak--Orlicz setting. In addition, under suitable assumptions on a growth function Φ, we prove that, for b∈ BMOΦ(ℝn), these commutators are bounded from the b-adapted Orlicz--Hardy space HbΦ(ℝn) to L1(ℝn) and from Orlicz Hardy space HΦ(ℝn) to L1,∞(ℝn).
Related
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BibTeX
@misc{han2026bmotype,
title = {{BMO-Type characterizations and endpoint estimates for commutators of intrinsic square functions on Orlicz-Hardy spaces}},
author = {Yanyan Han and Feng Liu and Yongming Wen and Huoxiong Wu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.15610},
eprint = {2609.15610},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15610},
}
RIS
TY - UNPB
TI - BMO-Type characterizations and endpoint estimates for commutators of intrinsic square functions on Orlicz-Hardy spaces
AU - Yanyan Han
AU - Feng Liu
AU - Yongming Wen
AU - Huoxiong Wu
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.15610
UR - https://arxiv.org/abs/2609.15610
AB - The commutators of intrinsic square functions associated with the intrinsic Littlewood--Paley g-function, the intrinsic g_λ^*-function and the intrinsic Lusin area function can be used to characterize BMO-type function spaces through their boundedness properties. In this paper, we show that, for b∈ BMO(ℝ^n), the boundedness of each of these commutators from the Musielak--Orlicz Hardy space H^φ(ℝ^n) to L^φ(ℝ^n) is equivalent to b∈ BMO_φ(ℝ^n) (a nontrivial subspace of BMO(ℝ^n)), under suitable assumptions on the growth function φ. This extends the weighted characterization of Han and Wu [Proc. Amer. Math. Soc. 152(1) (2024), 281--293] to the Musielak--Orlicz setting. In addition, under suitable assumptions on a growth function Φ, we prove that, for b∈ BMO_Φ(ℝ^n), these commutators are bounded from the b-adapted Orlicz--Hardy space H_b^Φ(ℝ^n) to L^1(ℝ^n) and from Orlicz Hardy space H^Φ(ℝ^n) to L^1,∞(ℝ^n).
ER -