On Lipschitz spaces in the Dunkl setting -- semigroup approach

2024/08/22 by Jacek Dziubański, Agnieszka Hejna, Dziubański, Jacek +1
Mathematics · #Mathematical Analysis and Transform Methods #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2408.12399

Abstract

Let \P_t\_t>0 be the Dunkl-Poisson semigroup associated with a root system R⊂ \mathbb R^N and a multiplicity function k≥ 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_tgt;0 t^m-β ‖(d^m)/(dt^m) P_tf‖_L^∞lt;∞, where m=[β]+1. We prove that the spaces Λ^β_k coincide with the classical Lipschitz spaces.

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