A generalization of the Littlewood-Paley inequality for the fractional Laplacian $(-\hat{I}”{)}^{\hat{I}\pm /2}$

Abstract

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