arXiv subjects
Publications and source records attributed to Rahmouni Atef.
The main purpose of this paper is to give an estimate for the Fourier Laguerre transform on Hardy spaces in the setting of Laguerre hypergroup. The atomic and molecular characterization is investigated which allows us to prove a version of Hormander's multiplier theorem on H^p (0<p\leq1).
A Paley type inequality for the Fourier transform on $H^p(H^n);$ the Hardy space on the Heisenberg group, is obtained for $0 < p \leq 1.$
\begin{abstract} For the Hardy space $H^p(\mathbb{R}^{d})$, $ 0<p\leq 1,$ we shall improve a Hardy's type inequality associated with Dunkl transform respect to the measures $dμ_{k}$ homogeneous of degree $γ,$ on the strip $(2γ+d)(2-p)\leqσ<2γ+d+p(N+1),$ where $N =[(2γ+d)(1/p-1)]$ is the greatest integer not exceeding $(2γ+d)(1/ p -1).$ \end{abstract}