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

Studia Mathematica (1995)

- Volume: 115, Issue: 3, page 207-217
- ISSN: 0039-3223

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topFan, Qihong. "Symbol calculus on the affine group "ax + b"." Studia Mathematica 115.3 (1995): 207-217. <http://eudml.org/doc/216208>.

@article{Fan1995,

abstract = {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.},

author = {Fan, Qihong},

journal = {Studia Mathematica},

keywords = {symbol calculus; Kirillov theory; orbits; Fuchs type pseudodifferential operators},

language = {eng},

number = {3},

pages = {207-217},

title = {Symbol calculus on the affine group "ax + b"},

url = {http://eudml.org/doc/216208},

volume = {115},

year = {1995},

}

TY - JOUR

AU - Fan, Qihong

TI - Symbol calculus on the affine group "ax + b"

JO - Studia Mathematica

PY - 1995

VL - 115

IS - 3

SP - 207

EP - 217

AB - 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.

LA - eng

KW - symbol calculus; Kirillov theory; orbits; Fuchs type pseudodifferential operators

UR - http://eudml.org/doc/216208

ER -

## References

top- [B] R. Beals, ${L}^{p}$ and Hölder estimates for pseudodifferential operators: Sufficient conditions, Ann. Inst. Fourier (Grenoble) 29 (3) (1979), 239-260. Zbl0387.35065
- [CM] R. Coifman et Y. Meyer, Au-delà des opérateurs pseudo-différentiels, Astérisque 57 (1978). Zbl0483.35082
- [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. Zbl0449.35002
- [K] A. A. Kirillov, Elements of the Theory of Representations, Springer, Berlin, 1976. Zbl0342.22001
- [U] A. Unterberger, The calculus of pseudodifferential operators of Fuchs type, Comm. Partial Differential Equations 9 (1984), 1179-1236. Zbl0561.35081
- [UU] A. Unterberger and H. Upmeier, Pseudodifferential analysis on symmetric cones, preprint, 1993.

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