Differential and Integral Equations

Pseudo-differential operator associated with the Dunkl operator

Abstract

In this paper, we establish that the pseudo-differential operator $T_{\sigma}$ associated with the Dunkl operator on the real line is bounded from $L_{p,\alpha}$ into itself for $1 < p < +\infty$, when the symbol $\sigma$ belongs to the class $S^{0}$.

Article information

Source
Differential Integral Equations, Volume 20, Number 9 (2007), 1035-1051.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356039310

Mathematical Reviews number (MathSciNet)
MR2349379

Zentralblatt MATH identifier
1211.47090

Citation

Abdelkefi, Chokri; Amri, Bechir; Sifi, Mohamed. Pseudo-differential operator associated with the Dunkl operator. Differential Integral Equations 20 (2007), no. 9, 1035--1051. https://projecteuclid.org/euclid.die/1356039310