Littlewood-Paley-Stein Functions for Hodge-de Rham and Schrodinger Operators

We study the Littlewood-Paley-Stein functions associated with Hodge-de Rham and Schrodinger operators on Riemannian manifolds. Under conditions on the Ricci curvature, we prove their boundedness on L-p for p in some interval (p(1), 2] and make a link to the Riesz Transform. An important fact is that we do not make assumptions of doubling measure or estimates on the heat kernel in this case. For p > 2, we give a criterion to obtain the boundedness of the vertical Littlewood-Paley-Stein function associated with Schrodinger operators on L-p.

Automated summary

The study focuses on the Littlewood-Paley-Stein functions associated with Hodge-de Rham and Schrodinger operators on Riemannian manifolds. Boundedness on L-p for p in some interval is proven under conditions on the Ricci curvature, while a link is made to the Riesz Transform. A criterion is provided to obtain the boundedness of the vertical Littlewood-Paley-Stein function associated with Schrodinger operators on L-p for p > 2.