## Tbilisi Mathematical Journal

### Multipliers and convolution spaces for the Hankel space and its dual on the half space $[0,+\infty [ \times\mathbb{R}^n$

C. Baccar

#### Abstract

We define the Hankel space $\mathbb{H}_\mu(]0,+\infty[\times\mathbb{R}^n)$; $\mu\geqslant -\frac{1}{2}$, and its dual $\mathbb{H'}_\mu(]0,+\infty[\times\mathbb{R}^n)$. First, we characterize the space $\mathscr{M}_\mu([0,+\infty[\times\mathbb{R}^n)$ of multipliers of the space $\mathbb{H}_\mu(]0,+\infty[\times\mathbb{R}^n)$. Next, we define a subspace $\mathbb{O}'_\mu([0,+\infty[\times \mathbb{R}^n)$ of the dual $\mathbb{H'}_\mu(]0,+\infty[\times\mathbb{R}^n)$ which permits to define and study a convolution product $\ast$ on $\mathbb{H'}_\mu(]0,+\infty[\times\mathbb{R}^n)$ and we give nice properties.

#### Article information

Source
Tbilisi Math. J., Volume 9, Issue 1 (2016), 197-220.

Dates
Received: 2 August 2015
Accepted: 10 January 2016
First available in Project Euclid: 12 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1528769046

Digital Object Identifier
doi:10.1515/tmj-2016-0009

Mathematical Reviews number (MathSciNet)
MR3486225

Zentralblatt MATH identifier
1337.42008

Subjects
Primary: 42B10: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
Secondary: 42B15: Multipliers

#### Citation

Baccar, C. Multipliers and convolution spaces for the Hankel space and its dual on the half space $[0,+\infty [ \times\mathbb{R}^n$. Tbilisi Math. J. 9 (2016), no. 1, 197--220. doi:10.1515/tmj-2016-0009. https://projecteuclid.org/euclid.tbilisi/1528769046