TY - JOUR
T1 - Pseudodifferential Operators Associated with a Semigroup of Operators
AU - Bernicot, Frédéric
AU - Frey, Dorothee
PY - 2014/2
Y1 - 2014/2
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 - http://www.scopus.com/inward/record.url?scp=84897023988&partnerID=8YFLogxK
U2 - 10.1007/s00041-013-9309-y
DO - 10.1007/s00041-013-9309-y
M3 - Article
SN - 1069-5869
VL - 20
SP - 91
EP - 118
JO - Journal of Fourier Analysis and Applications
JF - Journal of Fourier Analysis and Applications
IS - 1
ER -