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 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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In this paper we investigate how the short-time Fourier transform can be extended in a
Clifford setting. We prove some of the main properties of the Clifford short-time Fourier …

In this paper, we develop a new method based on the Laplace transform to study the Clifford-
Fourier transform. First, the kernel of the Clifford-Fourier transform in the Laplace domain is …

We introduce a generalized integral transform (GIT) whose integration path lies on the
complex plane. The GIT has both bilateral and unilateral versions, and generalizes a set of …

In this paper, we define and study a canonical Hardy-Littlewood-type maximal operator
associated with the one-dimensional generalized Fourier transform. For this operator to …

In this paper, we study the pointwise bounds for the kernel of the $(\kappa, a) $-generalized
Fourier transform with $\kappa\equiv0 $, introduced by Ben Sa\" id, Kobayashi and Orsted …

In this paper we present a family of solutions of the Clifford–Helmholtz system, which factors
the standard Helmholtz equation. All these solutions can be used as integral kernels of …