Pseudo-differential operator associated with the Dunkl operator. (English) Zbl 1211.47090

Abdelkefi, Chokri; Amri, Bechir; Sifi, Mohamed

Differ. Integral Equ. 20, No. 9, 1035-1051 (2007).

Summary: In this paper, we establish that the pseudodifferential 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 belongs to the class \(S^0\).

MSC:

47G30	Pseudodifferential operators
44A15	Special integral transforms (Legendre, Hilbert, etc.)
44A35	Convolution as an integral transform

Keywords:

pseudo-differential operator; Dunkl operator; boundedness