Hardy and Bmo Spaces on Graphs, Application to Riesz Transform

Joseph Feneuil

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)1-54
Number of pages54
JournalPotential Analysis
Issue number1
StatePublished - Jul 1 2016

Bibliographical note

Publisher Copyright:
© 2016, Springer Science+Business Media Dordrecht.


  • BMO spaces
  • Differential forms
  • Gaffney estimates
  • Graphs
  • Hardy spaces
  • Riesz transform


Dive into the research topics of 'Hardy and Bmo Spaces on Graphs, Application to Riesz Transform'. Together they form a unique fingerprint.

Cite this