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 $\mathbb R^d$.