On Lipschitz spaces in the Dunkl setting -- semigroup approach
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916366123008000 |
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| author | Dziubański, Jacek Hejna, Agnieszka |
| author_facet | Dziubański, Jacek Hejna, Agnieszka |
| contents | Let $\{P_t\}_{t>0}$ be the Dunkl-Poisson semigroup associated with a root system $R\subset \mathbb R^N$ and a multiplicity function $k\geq 0$. Analogously to the classical theory, we say that a bounded measurable function $f$ defined on $\mathbb R^N$ belongs to the inhomogeneous Lipschitz space $Λ_k^β$, $β>0$, if $$\sup_{t>0} t^{m-β} \Big\|\frac{d^m}{dt^m} P_tf\Big\|_{L^\infty}<\infty,$$ where $m=[β]+1$. We prove that the spaces $Λ^β_k$ coincide with the classical Lipschitz spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_12399 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Lipschitz spaces in the Dunkl setting -- semigroup approach Dziubański, Jacek Hejna, Agnieszka Functional Analysis 44A20, 42B20, 42B25, 47B38, 33C52, 39A70 Let $\{P_t\}_{t>0}$ be the Dunkl-Poisson semigroup associated with a root system $R\subset \mathbb R^N$ and a multiplicity function $k\geq 0$. Analogously to the classical theory, we say that a bounded measurable function $f$ defined on $\mathbb R^N$ belongs to the inhomogeneous Lipschitz space $Λ_k^β$, $β>0$, if $$\sup_{t>0} t^{m-β} \Big\|\frac{d^m}{dt^m} P_tf\Big\|_{L^\infty}<\infty,$$ where $m=[β]+1$. We prove that the spaces $Λ^β_k$ coincide with the classical Lipschitz spaces. |
| title | On Lipschitz spaces in the Dunkl setting -- semigroup approach |
| topic | Functional Analysis 44A20, 42B20, 42B25, 47B38, 33C52, 39A70 |
| url | https://arxiv.org/abs/2408.12399 |