On the range of a convolution operator in spaces of ultradifferentiable functions

We consider a nonsurjective convolution operator in the Beurling space of ultradifferentiable functions of mean type generated by the weight function $\omega$. We establish necessary and (separately) sufficient conditions on the symbol under which the range of the operator contains the space defined by another weight function and of another type. These results are applied to convolution operators in the Roumieu spaces of mean type.