Differential and Integral Equations

Pseudo-differential operator associated with the Dunkl operator

Chokri Abdelkefi, Bechir Amri, and Mohamed Sifi

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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

Subjects
Primary: 35S05: Pseudodifferential operators
Secondary: 44A15: Special transforms (Legendre, Hilbert, etc.) 44A35: Convolution 47G30: Pseudodifferential operators [See also 35Sxx, 58Jxx]

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.


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