Hardy and Bmo Spaces on Graphs, Application to Riesz Transform

Joseph Feneuil

doi:10.1007/s11118-016-9533-6

Hardy and Bmo Spaces on Graphs, Application to Riesz Transform

Joseph Feneuil

School of Mathematics

Research output: Contribution to journal › Article › peer-review

7 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 language	English (US)
Pages (from-to)	1-54
Number of pages	54
Journal	Potential Analysis
Volume	45
Issue number	1
DOIs	https://doi.org/10.1007/s11118-016-9533-6
State	Published - Jul 1 2016

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

Keywords

BMO spaces
Differential forms
Gaffney estimates
Graphs
Hardy spaces
Riesz transform

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10.1007/s11118-016-9533-6

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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.",

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N2 - 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.

AB - 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.

KW - BMO spaces

KW - Differential forms

KW - Gaffney estimates

KW - Graphs

KW - Hardy spaces

KW - Riesz transform

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UR - https://www.scopus.com/pages/publications/84975634997#tab=citedBy

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JO - Potential Analysis

JF - Potential Analysis

IS - 1

ER -

Hardy and Bmo Spaces on Graphs, Application to Riesz Transform

Abstract

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