Sub-Gaussian heat kernel estimates and quasi Riesz transforms for 1 ≤ p ≤ 2

Li Chen

doi:10.5565/PUBLMAT_59215_03

Sub-Gaussian heat kernel estimates and quasi Riesz transforms for 1 ≤ p ≤ 2

^*Corresponding author af dette arbejde

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avis › Tidsskriftartikel › Forskning › peer review

10 Citationer (Scopus)

Abstract

On a complete non-compact Riemannian manifold M, we prove that a so-called quasi Riesz transform is always Lp bounded for 1 < p ≤ 2. If M satisfies the doubling volume property and the sub-Gaussian heat kernel estimate, we prove that the quasi Riesz transform is also of weak type (1, 1).

Originalsprog	Engelsk
Tidsskrift	Publicacions Matematiques
Vol/bind	59
Nummer	2
Sider (fra-til)	313-338
Antal sider	26
ISSN	0214-1493
DOI	https://doi.org/10.5565/PUBLMAT_59215_03
Status	Udgivet - 2015
Udgivet eksternt	Ja

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abstract = "On a complete non-compact Riemannian manifold M, we prove that a so-called quasi Riesz transform is always Lp bounded for 1 < p ≤ 2. If M satisfies the doubling volume property and the sub-Gaussian heat kernel estimate, we prove that the quasi Riesz transform is also of weak type (1, 1).",

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AB - On a complete non-compact Riemannian manifold M, we prove that a so-called quasi Riesz transform is always Lp bounded for 1 < p ≤ 2. If M satisfies the doubling volume property and the sub-Gaussian heat kernel estimate, we prove that the quasi Riesz transform is also of weak type (1, 1).

KW - Heat semigroup

KW - Riemannian manifold

KW - Riesz transform

KW - Sub-Gaussian heat kernel estimates

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Sub-Gaussian heat kernel estimates and quasi Riesz transforms for 1 ≤ p ≤ 2

Abstract

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