In this paper we study a translation operator associated with the n-dimensional (k, 1)-
generalized Fourier transform, where k is a multiplicity function for the Dunkl operators. In …

In this paper, we discuss various basic properties of moduli of smoothness of functions from
L p (R d), 0< p≤∞. In particular, complete versions of Jackson-, Marchaud-, and Ulyanov …

The-generalised Fourier transform is the unitary operator defined using the-deformed Dunkl
harmonic oscillator. The main aim of this paper is to prove-boundedness of-generalised …

We study weighted (L p, L q)-boundedness properties of Riesz potentials and fractional
maximal functions for the Dunkl transform. In particular, we obtain the weighted Hardy …

A generalization of the Dunkl transform can be the-generalized Fourier transform, but it
deforms good classes of functions, for example, the Schwartz space. In this paper, we study …

We study the uncertainty principles related to the generalized Logan problem in R^d. We
define λ(f)=\sup{|x|:f(x)>0\} and τ(f)=\sup{|x|:x∈supp\,f\,\}. One of our main results provides …

On the real line, we study the generalized Dunkl harmonic analysis depending on a
parameter. The case of corresponds to the usual Dunkl harmonic analysis. All constructions …

We define a fractional power of the Dunkl Laplacian, a fractional modulus of smoothness,
and a fractional K-functional on L p-spaces with Dunkl weight. As an application, we extend …

A large family of Flett potentials is investigated. Formally, these potentials are negative
powers of the operators id+| x| 1− 1/m Δ k, where Δ k is the Dunkl Laplace (differential and …

In this paper we study direct and inverse approximation inequalities in L p (R d), 1< p<∞,
with the Dunkl weight. We obtain these estimates in their sharp form substantially improving …