Generalized Weinstein Sobolev–Gevrey spaces and pseudo-differential operators

• Published in: Rendiconti del Circolo matematico di Palermo Vol. 72; no. 1; pp. 273 - 292
• Main Authors: Ben Mohamed, Hassen, Chaffar, Mohamed Moktar
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.02.2023; Springer Nature B.V
• Subjects: Algebra; Analysis; Applications of Mathematics; Differential equations; Fluid mechanics; Geometry; Mathematics; Mathematics and Statistics; Operators (mathematics); Symbols; Generalized Weinstein transform; Generalized Weinstein operator; Pseudo-differential operators; Sobolev–Gevrey spaces
• ISSN: 0009-725X; 1973-4409
• DOI: 10.1007/s12215-021-00664-0

The first subject of this paper is to analyze and introduce a class of symbols and their associated pseudo-differential operators. In this case, we consider the generalized Weinstein operator Δ W d , α , n (for n = 0 , we regain the classical Weinstein operator Δ W α , d ). The Weinstein operator, mostly referred to as the Laplace–Bessel differential operator is now known as an important operator in analysis, because of its applications in pure and applied mathematics, especially in fluid mechanics. We introduce and study the Sobolev–Gevrey spaces associated with the generalized Weinstein operator and investigate their properties. Next, we introduce certain classes of symbols and their associated pseudo-differential operators. We show that these pseudo-differential operators naturally act on the generalized Weinstein Sobolev–Gevrey spaces.