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.
Department of Mathematics, Peking University, Beijing 100871, P.R. China
Bibliografia
[B] R. Beals, $L^p$ and Hölder estimates for pseudodifferential operators: Sufficient conditions, Ann. Inst. Fourier (Grenoble) 29 (3) (1979), 239-260.
[CM] R. Coifman et Y. Meyer, Au-delà des opérateurs pseudo-différentiels, Astérisque 57 (1978).
[CW] R. Coifman et G. Weiss, Analyse harmonique non-commutative sur certains espaces homogènes, Lecture Notes in Math. 242, Springer, Berlin, 1971.
[H] R. Howe, Quantum mechanics and partial differential equations, J. Funct. Anal. 38 (1980), 188-254.
[K] A. A. Kirillov, Elements of the Theory of Representations, Springer, Berlin, 1976.
[U] A. Unterberger, The calculus of pseudodifferential operators of Fuchs type, Comm. Partial Differential Equations 9 (1984), 1179-1236.
[UU] A. Unterberger and H. Upmeier, Pseudodifferential analysis on symmetric cones, preprint, 1993.