Littlewood--Paley--Stein Square Functions for the Fractional Discrete Laplacian on $\mathbb{Z}$

Huaiqian Li, Liying Mu

We investigate the boundedness of ``vertical'' Littlewood--Paley--Stein square functions for the nonlocal fractional discrete Laplacian on the lattice $\mathbb{Z}$, where the under…