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 for this work

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10 Citations (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).

Original language	English
Journal	Publicacions Matematiques
Volume	59
Issue	2
Pages (from-to)	313-338
Number of pages	26
ISSN	0214-1493
DOIs	https://doi.org/10.5565/PUBLMAT_59215_03
Publication status	Published - 2015
Externally published	Yes

Keywords

Heat semigroup
Riemannian manifold
Riesz transform
Sub-Gaussian heat kernel estimates

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10.5565/PUBLMAT_59215_03

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title = "Sub-Gaussian heat kernel estimates and quasi Riesz transforms for 1 ≤ p ≤ 2",

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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author = "Li Chen",

year = "2015",

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T1 - Sub-Gaussian heat kernel estimates and quasi Riesz transforms for 1 ≤ p ≤ 2

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N2 - 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).

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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U2 - 10.5565/PUBLMAT_59215_03

DO - 10.5565/PUBLMAT_59215_03

M3 - Journal article

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SN - 0214-1493

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SP - 313

EP - 338

JO - Publicacions Matematiques

JF - Publicacions Matematiques

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ER -

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

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Keywords

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