Littlewood-Paley-Stein functions for Hodge-de Rham and Schr{\"o}dinger operators
Analysis of PDEs
2019-12-19 v1
Abstract
We study the Littlewood-Paley-Stein functions associated with Hodge-de Rham and Schr{\"o}dinger 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 Schr{\"o}dinger operators on L p .
Keywords
Cite
@article{arxiv.1912.08471,
title = {Littlewood-Paley-Stein functions for Hodge-de Rham and Schr{\"o}dinger operators},
author = {Thomas Cometx},
journal= {arXiv preprint arXiv:1912.08471},
year = {2019}
}