A Weyl pseudodifferential calculus associated with exponential weights on $\mathbb{R}^d$

DOI10.1215/00192082-8886959arXiv2001.04572WikidataQ115517617 ScholiaQ115517617MaRDI QIDQ6332831

Sean Harris

Publication date: 13 January 2020

Abstract: We construct a Weyl pseudodifferential calculus tailored to studying boundedness of operators on weighted $L^p$ spaces over $mathbb{R}^d$ with weights of the form $exp(-phi(x))$, for $phi$ a $C^2$ function, a setting in which the operator associated to the weighted Dirichlet form typically has only holomorphic functional calculus. A symbol class giving rise to bounded operators on $L^p$ is determined, and its properties analysed. This theory is used to calculate an upper bounded on the $H^{i}nfty$ angle of relevant operators, and deduces known optimal results in some cases. Finally, the symbol class is enriched and studied under an algebraic viewpoint.

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) Functional calculus for linear operators (47A60) Linear operators on function spaces (general) (47B38)

This page was built for publication: A Weyl pseudodifferential calculus associated with exponential weights on $\mathbb{R}^d$

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6332831)