Marcinkiewicz multipliers and multi-parameter structure on Heisenberg (-type) groups, II

Mathematische Zeitschrift

Volumn 221, Issue 1, 1996, Pages 267-291

  Müller, Detlef ^a   Ricci, Fulvio ^b   Stein, Elias M ^c  

^a UNIVERSITY OF KIEL   (Germany)

^b POLITECNICO DI TORINO   (Italy)

^c PRINCETON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 17444446679     PISSN: 00255874     EISSN: None     Source Type: Journal    
DOI: 10.1007/bf02622116     Document Type: Article

References (21)

1. Carbery, A., Seeger, A.: Homogeneous Fourier multipliers of Marcinkiewicz type. (preprint)
2. Christ, M.: The strong maximal function on a nilpotent group. Trans. Amer. Math. Soc. 331, 1-13 (1992)
3. Cowling, M., Dooley, A.H., Koranyi, A., Ricci, F.: H-type groups and Iwasawa decompositions. Advances in Math. 87, 1-41 (1991)
4. Damek, E., Ricci, F.: Harmonic analysis on solvable extensions of H-type groups. J. Geom. Anal. 2, 213-248 (1992)
5. Erdelyi, A., Magnus, W., Oberhettinger, F., Tricomi, F.G.: Higher transcendental functions. Mc Graw-Hill, New York, 1953
6. Folland, G.B., Stein, E.M.: Hardy spaces on homogeneous groups. Princeton Univ. Press, N.J., 1982
7. Gasper, G., Trebels, W.: A characterization of localized Bessel potential spaces and applications to Jacobi and Hankel multipliers. Studia Math. LXV, 243-278 (1979)
8. Hebisch, W.: Multiplier theorem on generalized Heisenberg groups. Colloquium Math. LXV, 231-239 (1993)
9. Helffer, B., Nourrigat, J.: Caractérisation des opérateurs hypoelliptiques homogènes invariants à gauche sur un groupe de Lie nilpotent gradué. Comm. in Partial Diff. Eq. 4, 899-958 (1979)
10. Hulanicki, A.: A functional calculus for Rockland operators on nilpotent Lie groups. Studia Math. 78, 253-266 (1984)
11. Kaplan, A.: Fundamental solutions for a class of hypoelliptic p.d.e. generated by composition of quadratic forms. Trans. Amer. Math. Soc. 258, 147-153 (1980)
12. Mauceri, G.: Maximal operators and Riesz means on stratified groups. Symposia Math. XXIX, 46-62
13. Metivier, G.: Hypoelliticité analytique sur des groupes nilpotents de rang 2. Duke Math. J. 47, 195-221 (1980)
14. Müller, D., Ricci, F.: Solvability for a class of doubly characteristic differential operators on 2-step nilpotent groups. (to appear in Annals of Math)
15. Müller D., Ricci, F., Stein, E.M.: Marcinkiewicz multipliers and two-parameter structures on Heisenberg groups I. Invent. Math. 119, 199-233 (1995)
16. Müller, D., Stein, E.M.: On spectral multipliers for Heisenberg and related groups. J. Math. Pures Appl. 73, 413-440 (1994)
17. Ricci, F.: Harmonic analysis on generalized Heisenberg groups. (unpublished preprint)
18. Ricci, F., Sjögren, P.: Two-parameter maximal functions in the Heisenberg group. Math. Zeitschrift 199, 565-575 (1988)
19. Stein, E.M.: Singular integrals and differentiability properties of functions. Princeton Univ. Press, N.J., 1970
20. Stein, E.M., Weiss, G.: Introduction to Fourier analysis on Euclidean spaces. Princeton Univ. Press, 1971
21. p harmonic analysis and Radon transforms on the Heisenberg group. J. Funct. Anal. 96, 350-406 (1991)