We investigate properties of pseudodifferential operators on $L^2$ space on manifold with ends including asymptotically conical or hyperbolic ends. Our pseudodifferential operators are a generalization of the canonical quantization which naturally appears in the quantum mechanics on curved spaces. We prove a Calder\'on-Vaillancourt type theorem for our pseudodifferential operators and discuss a construction of parametrix of elliptic differential operators on manifolds with ends.
Chemotaxis effect vs logistic damping on boundedness in the 2-D minimal Keller-Segel model
On a class of $h$-Fourier integral operators
Boundedness of maximal functions on non-doubling manifolds with ends
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