Hardy spaces and heat kernel regularity

In this paper, we show the equivalence between the boundedness of the Riesz transform $d\Delta^{-1/2}$ on $L^p$, $p\in (2,p_0)$, and the equality $H^p=L^p$, $p\in(2,p_0)$, in the class of manifold whose measure is doubling and for which the scaled Poincar\'{e} inequalities hold. Here, $H^p$ is a Hardy space of exact $1-$forms, naturally associated with the Riesz transform.

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Field Value
Source https://hal.science/hal-00854582
Author Devyver, Baptiste
Maintainer CCSD
Last Updated May 10, 2026, 00:14 (UTC)
Created May 10, 2026, 00:14 (UTC)
Identifier hal-00854582
Language en
Rights https://about.hal.science/hal-authorisation-v1/
contributor Department of Mathematics (TECHNION) ; Technion - Israel Institute of Technology [Haifa]
creator Devyver, Baptiste
date 2013-08-27T00:00:00
harvest_object_id 82e86d8d-c4e4-4d91-b160-eff92d768cf3
harvest_source_id 3374d638-d20b-4672-ba96-a23232d55657
harvest_source_title test moissonnage SELUNE
metadata_modified 2024-04-22T00:00:00
relation info:eu-repo/semantics/altIdentifier/arxiv/1308.5871
set_spec type:UNDEFINED