Abstract
We construct a Weyl pseudodifferential calculus tailored to studying boundedness of operators on weighted Lp spaces over Rd with weights of the form exp(−ϕ(x)), for ϕ a C2 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 Lp is determined, and its properties are analyzed. This theory is used to calculate an upper bounded on the H∞ angle of relevant operators and deduces known optimal results in some cases. Finally, the symbol class is enriched and studied under an algebraic viewpoint.
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