Hardy and Bmo Spaces on Graphs, Application to Riesz Transform

Joseph Feneuil

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

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)
JournalPotential Analysis
Volume45
Issue number1
DOIs
StatePublished - Jul 1 2016

Bibliographical note

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

Copyright:
Copyright 2016 Elsevier B.V., All rights reserved.

Keywords

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

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