Endpoint estimates for commutators of singular integral operators associated with admissible functions

Abstract

Let (𝒳, d, μ) be a space of homogeneous type and let ρ be an admissible function on 𝒳. In this paper, we introduce a new class of singular integral operators associated with ρ, including a wide range of operators arising in harmonic analysis. For such an operator T and a function b belonging to suitable localized BMO spaces associated with ρ, which are strictly larger than the classical space BMO(𝒳), we establish the boundedness of the commutator $[b, T]$ from the Hardy space H¹_ρ(𝒳) into L^1,∞(𝒳), L¹(𝒳), and H¹_ρ(𝒳). Moreover, the boundedness of [b,T] on H¹_ρ(𝒳) is characterized by necessary and sufficient conditions. We then apply this to investigate the boundedness of commutators of singular integrals in various settings, including Schrödinger operators on stratified Lie groups and Laguerre operators of convolution type. Our results are new even for Schrödinger operators on ℝⁿ.

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BibTeX RIS

BibTeX

@misc{bui2026endpoint,
  title = {{Endpoint estimates for commutators of singular integral operators associated with admissible functions}},
  author = {The Anh Bui and Xuan Thinh Duong and Luong Dang Ky},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.23662},
  eprint = {2609.23662},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.23662},
}

RIS

TY  - UNPB
TI  - Endpoint estimates for commutators of singular integral operators associated with admissible functions
AU  - The Anh Bui
AU  - Xuan Thinh Duong
AU  - Luong Dang Ky
PY  - 2026
DA  - 2026/09/20
PB  - arXiv
DO  - 10.48550/arxiv.2609.23662
UR  - https://arxiv.org/abs/2609.23662
AB  - Let (𝒳, d, μ) be a space of homogeneous type and let ρ be an admissible function on 𝒳. In this paper, we introduce a new class of singular integral operators associated with ρ, including a wide range of operators arising in harmonic analysis. For such an operator T and a function b belonging to suitable localized BMO spaces associated with ρ, which are strictly larger than the classical space BMO(𝒳), we establish the boundedness of the commutator $[b, T]$ from the Hardy space H^1_ρ(𝒳) into L^1,∞(𝒳), L^1(𝒳), and H^1_ρ(𝒳). Moreover, the boundedness of [b,T] on H^1_ρ(𝒳) is characterized by necessary and sufficient conditions. We then apply this to investigate the boundedness of commutators of singular integrals in various settings, including Schrödinger operators on stratified Lie groups and Laguerre operators of convolution type. Our results are new even for Schrödinger operators on ℝ^n.
ER  -

Abstract

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