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Dunkl--BMO functions representable in terms of generalized balayage of Carleson measures and an application

  • Qingdong Guo
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Abstract

We characterize compactly supported functions f in Dunkl--BMO spaces as those that can be written as f=g+S̃μ,𝒫, the sum of some bounded function g and the generalized balayage S̃μ,𝒫 of a Carleson measure on ℝN×(0,∞) associated with the Dunkl--Poisson semigroup. As a direct application of this representation of Dunkl--BMO functions, we establish a new characterization of the Hardy space in the Dunkl setting via a principal value integral related to S̃μ,𝒫. Moreover, analogous conclusions hold for the Dunkl--heat semigroup as well.

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Cite

BibTeXRIS
BibTeX
@misc{guo2026dunklbmo,
  title = {{Dunkl--BMO functions representable in terms of generalized balayage of Carleson measures and an application}},
  author = {Qingdong Guo},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.05092},
  eprint = {2610.05092},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.05092},
}
RIS
TY  - UNPB
TI  - Dunkl--BMO functions representable in terms of generalized balayage of Carleson measures and an application
AU  - Qingdong Guo
PY  - 2026
DA  - 2026/10/22
PB  - arXiv
DO  - 10.48550/arxiv.2610.05092
UR  - https://arxiv.org/abs/2610.05092
AB  - We characterize compactly supported functions f in Dunkl--BMO spaces as those that can be written as f=g+S̃_μ,𝒫, the sum of some bounded function g and the generalized balayage S̃_μ,𝒫 of a Carleson measure on ℝ^N×(0,∞) associated with the Dunkl--Poisson semigroup. As a direct application of this representation of Dunkl--BMO functions, we establish a new characterization of the Hardy space in the Dunkl setting via a principal value integral related to S̃_μ,𝒫. Moreover, analogous conclusions hold for the Dunkl--heat semigroup as well.
ER  -