On the solution of the Cauchy problem in the weighted spaces of Beurling   ultradistributions
  Results of Da Prato and Sinestrari, on differential operators with non-dense domain but satisfying the Hille--Yosida condition, are applied in the setting of Beurling weighted spaces of ultradistributions   $\DD'^{(s)}_{L^p}((0,T)\times U)$, where $U$ is open and bounded set in $\mathbb R^d$. 
Stevan Pilipovi\' c, Bojan Prangoski and Daniel Velinov
math.FA