Open Access
Translator Disclaimer
June 2016 Multipliers and convolution spaces for the Hankel space and its dual on the half space $[0,+\infty [ \times\mathbb{R}^n$
C. Baccar
Author Affiliations +
Tbilisi Math. J. 9(1): 197-220 (June 2016). DOI: 10.1515/tmj-2016-0009

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.

Citation

Download Citation

C. Baccar. "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 (1) 197 - 220, June 2016. https://doi.org/10.1515/tmj-2016-0009

Information

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

zbMATH: 1337.42008
MathSciNet: MR3486225
Digital Object Identifier: 10.1515/tmj-2016-0009

Subjects:
Primary: 42B10
Secondary: 42B15

Rights: Copyright © 2016 Tbilisi Centre for Mathematical Sciences

JOURNAL ARTICLE
24 PAGES


SHARE
Vol.9 • No. 1 • June 2016
Back to Top