{\L}ojasiewicz ideals in Denjoy-Carleman classes
  The classical notion of {\L}ojasiewicz ideals of smooth functions is studied in the context of non-quasianalytic Denjoy-Carleman classes. In the case of principal ideals, we obtain a characterization of {\L}ojasiewicz ideals in terms of properties of a generator. This characterization involves a certain type of estimates that differ from the usual {\L}ojasiewicz inequality. We then show that basic properties of {\L}ojasiewicz ideals in the $\mathcal{C}^\infty$ case have a Denjoy-Carleman counterpart. 
Vincent Thilliez
math.CA math.FA