Fractional powers of the parabolic Hermite operator. Regularity properties

Marta de León-Contreras, José L. Torrea

Let $\mathcal{L}={\partial }_t-{\Delta }_x+|x{|}^2$. Consider its Poisson semigroup $e^{-y\sqrt{\mathcal{L}}}$. For $\alpha >0$ define the Parabolic Hermite-Zygmund spaces $$ Λ^α_{\mathcal{L}}=\lef…