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Hardy and Bmo Spaces on Graphs, Application to Riesz Transform

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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 H 1 Hardy spaces of functions and 1-forms adapted to P and prove various characterizations of these spaces. We also characterize the dual space of H 1 as a BMO-type space adapted to P. As an application, we establish H 1 and H 1- L 1 boundedness of the Riesz transform.

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Authors and Affiliations

  1. Saint Martin d’Hères Cedex, Institut Fourier, 100 rue des mathématiques, BP74, 38402, Cedex, France

    Joseph Feneuil

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  1. Joseph Feneuil
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Correspondence to Joseph Feneuil.

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Feneuil, J. Hardy and Bmo Spaces on Graphs, Application to Riesz Transform. Potential Anal 45, 1–54 (2016). https://doi.org/10.1007/s11118-016-9533-6

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  • DOI: https://doi.org/10.1007/s11118-016-9533-6

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