Stratified Whitney jets and tempered ultradistributions on the subanalytic site

We will start by introducing the subanalytic sheaf of stratified Whitney jets with Gevrey growth conditions, $\mathcal{SW}^*$. It is the counterpart of classical Whitney jets with Gevrey conditions in the context of subanalytic sheaves. Then we will give an explicit description of the dual of the global sections of $\mathcal{SW}^*$. By means of this dual we will define the subanalytic presheaf of stratified ultradistributions which satisfies the two following properties. Its sections on certains good sets coincide with sections of tempered ultradistributions and it is a subanalytic sheaf in dimension 2. This subject is a joint work with N. Honda (Hokkaido University).