Symbol calculus on the affine group "ax + b"

Qihong Fan

Studia Mathematica (1995)

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

Abstract

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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.

How to cite

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Fan, 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

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  1. [B] R. Beals, L p and Hölder estimates for pseudodifferential operators: Sufficient conditions, Ann. Inst. Fourier (Grenoble) 29 (3) (1979), 239-260. Zbl0387.35065
  2. [CM] R. Coifman et Y. Meyer, Au-delà des opérateurs pseudo-différentiels, Astérisque 57 (1978). Zbl0483.35082
  3. [CW] R. Coifman et G. Weiss, Analyse harmonique non-commutative sur certains espaces homogènes, Lecture Notes in Math. 242, Springer, Berlin, 1971. 
  4. [H] R. Howe, Quantum mechanics and partial differential equations, J. Funct. Anal. 38 (1980), 188-254. Zbl0449.35002
  5. [K] A. A. Kirillov, Elements of the Theory of Representations, Springer, Berlin, 1976. Zbl0342.22001
  6. [U] A. Unterberger, The calculus of pseudodifferential operators of Fuchs type, Comm. Partial Differential Equations 9 (1984), 1179-1236. Zbl0561.35081
  7. [UU] A. Unterberger and H. Upmeier, Pseudodifferential analysis on symmetric cones, preprint, 1993. 

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