A generalization of the Littlewood-Paley inequality for the fractional Laplacian $(-\Delta {)}^{\alpha /2}$

Ildoo Kim, Kyeong-Hun Kim

We prove a parabolic version of the Littlewood-Paley inequality for the fractional Laplacian $(-\Delta {)}^{\alpha /2}$, where $\alpha \in (0,2)$.