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 …

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 …

We first study the Lipschitz spaces Λ d β associated with the Dunkl metric, β∈(0, 1), and
prove that it is a proper subspace of the classical Lipschitz spaces Λ β on RN, as the Dunkl …

In this paper we present a new approach to vector-valued singular integrals, which allows us
to obtain the Lp-estimates for vector valued Dunklmaximal functions and analogue of the …

In this paper we study certain relations between the Dunkl–Sobolev classes of fractional
order L α, kp (IR) and the generalized Dunkl–Lipschitz classes∧ α, p, qk (IR). Next, we show …

We discuss in which cases the Dunkl convolution of distributions, possibly both with non-
compact support, can be defined and study its analytic properties. We prove results on the …

Duality of generalized Dunkl-Lipschitz spaces Page 1 Acta Mathematica Scientia 2017,37B(6):1567–1593
http://actams.wipm.ac.cn DUALITY OF GENERALIZED DUNKL-LIPSCHITZ SPACES∗ …

The purpose of this paper is to introduce a new class of singular integral operators in the
Dunkl setting which is associated with finite reflection groups on the Euclidean space. The …

In the present paper, we have studied the Dunkl–Hausdorff operators Hα, ϕ on the Dunkl-
type homogeneous weighted Herz spaces K β, p α, q and Dunkl Herz-type Hardy space HK …