On the Range of Two Convolution Operators

Let _(ω)(?) denote the non–quasianalytic class of Beurling type on ?. For μ, ν ∈ ′_(ω)(?) we give necessary conditions for the inclusion T_ν( _(ω)(?)) ? T_μ( _(ω)(?)), thus extending previous work of Malgrange and Ehrenpreis .