### Symbol calculus on the affine group "ax + b"

The symbol calculus on the upper half plane is studied from the viewpoint of the Kirillov theory of orbits. The main result is the ${L}^{p}$-estimates for Fuchs type pseudodifferential operators.

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The symbol calculus on the upper half plane is studied from the viewpoint of the Kirillov theory of orbits. The main result is the ${L}^{p}$-estimates for Fuchs type pseudodifferential operators.

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