Let Γ be a graph with the doubling property for the volume of balls and P a reversible random walk on Γ. We introduce H1 Hardy spaces of functions and 1-forms adapted to P and prove various characterizations of these spaces. We also characterize the dual space of H1 as a BMO-type space adapted to P. As an application, we establish H1 and H1- L1 boundedness of the Riesz transform.
Bibliographical notePublisher Copyright:
© 2016, Springer Science+Business Media Dordrecht.
Copyright 2016 Elsevier B.V., All rights reserved.
- BMO spaces
- Differential forms
- Gaffney estimates
- Hardy spaces
- Riesz transform