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 …

We obtain several versions of the Hausdorff–Young and Hardy–Littlewood inequalities for
the (k, a)-generalized Fourier transform recently investigated at length by Ben Saïd …

In this paper, we present the basic k-Hankel wavelet theory. Next, we study the
boundedness and compactness of localization operators associated with k-Hankel wavelet …

We introduce the notion of the (k, a)-generalized wavelet multipliers. Particular cases of such
generalized wavelet multipliers are the classical and Dunkl wavelet multipliers. The …

In this paper, we introduce a family of one-dimensional maximal operators M κ, m, κ≥ 0 and
m∈ N∖{0}, which includes the Hardy–Littlewood maximal operator as a special case (κ= 0 …

A product formula and a convolution structure for a k-Hankel transform on R - ScienceDirect Skip
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We introduce the notion of the (k, a)-generalized wavelet transform. Particular cases of such
generalized wavelet transform are the classical and the Dunkl wavelet transforms. The …

In this paper, we introduce and we study the k-Hankel Gabor transform on R^ d R d with
radial windows. We investigate for this transform the general theory of reproducing kernels …

Let $\Delta_ {k, a} $ and $\Delta_k $ be the $(k, a) $-generalized Laguerre operator and the
Dunkl Laplacian operator on $\mathbb {R}^ n $, respectively. The aim of this article is …

We introduce the notion of ak-Laguerre two-wavelet multiplier, and we give its trace formula
as a bounded linear operator in the trace class from into in terms of the symbol and the two …