The aims of these lecture notes are twofold. On the one hand, they are meant as an
introduction to rational and trigonometric Dunkl theory, starting with the historical examples …

In this work we extend the theory of the classical Hardy space H^ 1 H 1 to the rational Dunkl
setting. Specifically, let Δ Δ be the Dunkl Laplacian on a Euclidean space R^ N RN. On the …

For a normalized root system R in RN and a multiplicity function k≥ 0 let N= N+∑ α∈ R k
(α). Denote by dw (x)=∏ α∈ R|< x, α>| k (α) dx the associated measure in R N. Let F stand …

The purpose of this paper is to introduce a new class of singular integral operators in the
Dunkl setting involving both the Euclidean metric and the Dunkl metric. Then we provide the …

On RN equipped with a root system R and a multiplicity function k> 0, we study the
generalized (Dunkl) translations τ xg (-y) of not necessarily radial kernels g. Under certain …

In this paper we study the Sobolev inequality in the Dunkl setting using two new approaches
which provide a simpler elementary proof of the classical case p= 2, as well as an extension …

The rational Dunkl operators are commuting differential-reflection operators on the
Euclidean space R d associated with a root system, that contain some non-local refection …

In this paper we characterise the pointwise size and regularity estimates for the Dunkl Riesz
transform kernel involving both the Euclidean metric and the Dunkl metric, where these two …

Abstract On RN R^N equipped with a root system R, multiplicity function k≥ 0 k≥0, and the
associated measure dw (x)=∏ α∈ R|⟨ x, α⟩| k (α) dx dw(x)=∏_α∈R|⟨x,α⟩|^k(α)\,dx, we …

Liflyand and Móricz in Liflyand and Móricz [The Hausdorff operator is bounded on the real
Hardy space H 1 (R). Proc Amer Math Soc. 1999; 128: 1391–1396; Commuting relations for …