Symbol calculus on the affine group "ax + b"

• Autorzy: Qihong Fan
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 22E30: Analysis on real and complex Lie groups
• 43A85: Analysis on homogeneous spaces
• 42B20: Singular and oscillatory integrals (Calder\'on-Zygmund, etc.)
• 35S05: Pseudodifferential operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1995
• Tom: 115
• Numer: 3
• Strony: 207-217

Daty

wydano

1995

otrzymano

1994-04-11

poprawiono

1994-12-04

Twórcy

autor

Qihong Fan

• 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.