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Pré-Publication, Document De Travail Année : 2015

Riesz transform on graphs under subgaussian estimates

Joseph Feneuil
  • Fonction : Auteur

Résumé

Let Γ be a doubling graph satisfying some pointwise subgaussian estimates of the Markov kernel. We introduce a space $H^1(\Gamma)$ of functions and a space $H^1(T_\Gamma)$ of 1-forms and give various characterizations of them. We prove the $H^1$-boundedness of the Riesz transform, from which we deduce the $L^p$ boundedness of the Riesz transform for any $p\in (1,2)$. Note that in [1, Theorem 1.40], we showed a $H^1_w$-boundedness of the Riesz transform under weaker assumptions, but the $L^p$ boundedness was not established. [1] J. Feneuil, Hardy and BMO spaces on graphs, application to Riesz transform, 2014, preprint hal-01074559.
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Dates et versions

hal-01167446 , version 1 (24-06-2015)

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Joseph Feneuil. Riesz transform on graphs under subgaussian estimates. 2015. ⟨hal-01167446⟩

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