Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

On Lipschitz spaces in the Dunkl setting -- semigroup approach (2408.12399v1)

Published 22 Aug 2024 in math.FA

Abstract: Let ${P_t}{t>0}$ be the Dunkl-Poisson semigroup associated with a root system $R\subset \mathbb RN$ and a multiplicity function $k\geq 0$. Analogously to the classical theory, we say that a bounded measurable function $f$ defined on $\mathbb RN$ belongs to the inhomogeneous Lipschitz space $\Lambda_k\beta$, $\beta>0$, if $$\sup{t>0} t{m-\beta} \Big|\frac{dm}{dtm} P_tf\Big|_{L\infty}<\infty,$$ where $m=[\beta]+1$. We prove that the spaces $\Lambda\beta_k$ coincide with the classical Lipschitz spaces.

Summary

We haven't generated a summary for this paper yet.