Almost periodic pseudodifferential operators and Gevrey classes

作者：Oliaro Alessandro^*; Rodino Luigi; Wahlberg Patrik

来源：Annali di Matematica Pura ed Applicata, 2012, 191(4): 725-760.

DOI：10.1007/s10231-011-0203-4

• Pseudodifferential calculus
• Almost periodic functions
• Gevrey classes
• Gevrey hypoellipticity

We study almost periodic pseudodifferential operators acting on almost periodic functions G(ap)(s) (R-d) of Gevrey regularity index s %26gt;= 1. We prove that almost periodic operators with symbols of Hormander type S-rho,delta(m) satisfying an s-Gevrey condition are continuous on G(ap)(s) (R-d) provided 0 %26lt; rho %26lt;= 1, delta = 0 and s rho %26gt;= 1. A calculus is developed for symbols and operators using a notion of regularizing operator adapted to almost periodic Gevrey functions and its duality. We apply the results to show a regularity result in this context for a class of hypoelliptic operators.

• 出版日期2012-12