Pseudodifferential Operators Associated with a Semigroup of Operators

Frédéric Bernicot; Dorothee Frey

doi:10.1007/s00041-013-9309-y

Pseudodifferential Operators Associated with a Semigroup of Operators

Frédéric Bernicot^*, Dorothee Frey

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

Related to a semigroup of operators on a metric measure space, we define and study pseudodifferential operators (including the setting of Riemannian manifolds, fractals, graphs etc.). Boundedness on L ^p for pseudodifferential operators of order 0 is proved. We mainly focus on symbols belonging to the class S⁰_{1, δ} for δ∈[0,1). For the limit class S⁰_1,1, we describe some results by restricting our attention to the case of a sub-Laplacian operator on a Riemannian manifold.

Original language	English
Pages (from-to)	91-118
Number of pages	28
Journal	Journal of Fourier Analysis and Applications
Volume	20
Issue number	1
DOIs	https://doi.org/10.1007/s00041-013-9309-y
Publication status	Published - Feb 2014

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abstract = "Related to a semigroup of operators on a metric measure space, we define and study pseudodifferential operators (including the setting of Riemannian manifolds, fractals, graphs etc.). Boundedness on L p for pseudodifferential operators of order 0 is proved. We mainly focus on symbols belonging to the class S01, δ for δ∈[0,1). For the limit class S01,1, we describe some results by restricting our attention to the case of a sub-Laplacian operator on a Riemannian manifold.",

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AU - Bernicot, Frédéric

AU - Frey, Dorothee

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N2 - Related to a semigroup of operators on a metric measure space, we define and study pseudodifferential operators (including the setting of Riemannian manifolds, fractals, graphs etc.). Boundedness on L p for pseudodifferential operators of order 0 is proved. We mainly focus on symbols belonging to the class S01, δ for δ∈[0,1). For the limit class S01,1, we describe some results by restricting our attention to the case of a sub-Laplacian operator on a Riemannian manifold.

AB - Related to a semigroup of operators on a metric measure space, we define and study pseudodifferential operators (including the setting of Riemannian manifolds, fractals, graphs etc.). Boundedness on L p for pseudodifferential operators of order 0 is proved. We mainly focus on symbols belonging to the class S01, δ for δ∈[0,1). For the limit class S01,1, we describe some results by restricting our attention to the case of a sub-Laplacian operator on a Riemannian manifold.

KW - Heat semigroup

KW - Metric measure space

KW - Pseudodifferential operators

UR - https://www.scopus.com/pages/publications/84897023988

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DO - 10.1007/s00041-013-9309-y

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EP - 118

JO - Journal of Fourier Analysis and Applications

JF - Journal of Fourier Analysis and Applications

IS - 1

ER -

Pseudodifferential Operators Associated with a Semigroup of Operators

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