Translation operator and maximal function for the (k, 1)-generalized Fourier transform
SB Saïd, L Deleaval - Journal of Functional Analysis, 2020 - Elsevier
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 …
generalized Fourier transform, where k is a multiplicity function for the Dunkl operators. In …
Weighted inequalities and uncertainty principles for the -generalized Fourier transform
TR Johansen - International Journal of Mathematics, 2016 - World Scientific
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 …
the (k, a)-generalized Fourier transform recently investigated at length by Ben Saïd …
Norm inequalities for maximal operators
S Ben Said, S Negzaoui - Journal of Inequalities and Applications, 2022 - Springer
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 …
m∈ N∖{0}, which includes the Hardy–Littlewood maximal operator as a special case (κ= 0 …
[HTML][HTML] A product formula and a convolution structure for a k-Hankel transform on R
SB Saïd - Journal of Mathematical Analysis and Applications, 2018 - Elsevier
A product formula and a convolution structure for a k-Hankel transform on R - ScienceDirect Skip
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On the Clifford short-time Fourier transform and its properties
A De Martino - Applied Mathematics and Computation, 2022 - Elsevier
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 …
Clifford setting. We prove some of the main properties of the Clifford short-time Fourier …
A new construction of the Clifford-Fourier kernel
D Constales, H De Bie, P Lian - Journal of Fourier Analysis and …, 2017 - Springer
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 …
Fourier transform. First, the kernel of the Clifford-Fourier transform in the Laplace domain is …
[HTML][HTML] A transition integral transform obtained from generalization of the Fourier transform
RG Gonzalez-Acuna, JC Gutierrez-Vega - Ain Shams Engineering Journal, 2019 - Elsevier
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 …
complex plane. The GIT has both bilateral and unilateral versions, and generalizes a set of …
[PDF][PDF] A Hardy–Littlewood maximal operator for the generalized Fourier transform on
SB Saïd, L Deleaval - J. Geom. Anal., 2020 - perso.math.u-pem.fr
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 …
associated with the one-dimensional generalized Fourier transform. For this operator to …
Bounds for the kernel of the -generalized Fourier transform
H De Bie, P Lian, F Maes - arXiv preprint arXiv:2310.14229, 2023 - arxiv.org
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 …
Fourier transform with $\kappa\equiv0 $, introduced by Ben Sa\" id, Kobayashi and Orsted …
Fourier Kernels Associated with the Clifford–Helmholtz System
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 …
the standard Helmholtz equation. All these solutions can be used as integral kernels of …