| Title:
|
On Besov spaces and absolute convergence of the Fourier transform on Heisenberg groups (English) |
| Author:
|
Skrzypczak, Leszek |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
39 |
| Issue:
|
4 |
| Year:
|
1998 |
| Pages:
|
755-763 |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper the absolute convergence of the group Fourier transform for the Heisenberg group is investigated. It is proved that the Fourier transform of functions belonging to certain Besov spaces is absolutely convergent. The function spaces are defined in terms of the heat semigroup of the full Laplacian of the Heisenberg group. (English) |
| Keyword:
|
Besov spaces |
| Keyword:
|
Heisenberg groups |
| Keyword:
|
group Fourier transform |
| MSC:
|
22E25 |
| MSC:
|
43A30 |
| MSC:
|
43A80 |
| MSC:
|
46E35 |
| idZBL:
|
Zbl 1060.46512 |
| idMR:
|
MR1715464 |
| . |
| Date available:
|
2009-01-08T18:48:18Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119050 |
| . |
| Reference:
|
[1] Bernstein S.: Sur la convergence absolute des séries trigonométriques.C.R.A.S. Paris 158 (1994), 1661-1664. |
| Reference:
|
[2] Coulhon T., Saloff-Coste L.: Semi-groupes d'opérateurs et espaces fonctionels sur les groupes de Lie.J. Approx. Theory 65 (1991), 176-198. MR 1104158 |
| Reference:
|
[3] Folland G.: Harmonic analysis in phase space.Ann. Math. Stud. 112, Princeton Univ. Press, 1989. Zbl 0682.43001, MR 0983366 |
| Reference:
|
[4] Gaudry G.I., Meda S., Pini R.: A heat semigroup version of Bernstein's theorem on Lie groups.Monatshefte Math. 110 (1990), 101-115. Zbl 0719.43008, MR 1076325 |
| Reference:
|
[5] Geller D.: Fourier analysis on the Heisenberg group.J. Funct. Anal. 36 (1980), 205-254. Zbl 0433.43008, MR 0569254 |
| Reference:
|
[6] Geller D.: Spherical harmonics, the Weyl transform and the Fourier transform on the Heisenberg group.Canad. J. Math. 36 (1984), 615-684. Zbl 0596.46034, MR 0756538 |
| Reference:
|
[7] Herz C.: Lipschitz spaces and Bernstein's theorem on absolutely convergent Fourier transform.J. Math. Mechanics 18 (1968), 283-324. MR 0438109 |
| Reference:
|
[8] Inglis I.R.: Bernstein's theorem and the Fourier algebra of the Heisenberg group.Boll. Un. Mat. Ital. 6 (1983), 39-46. Zbl 0528.43008, MR 0694742 |
| Reference:
|
[9] Saka K.: Besov spaces and Sobolev spaces on a nilpotent Lie group.Tôhoku Math. J. 31 (1979), 383-437. Zbl 0429.43004, MR 0558675 |
| Reference:
|
[10] Skrzypczak L.: Atomic decompositions on Riemannian manifolds with bounded geometry.Forum Math. 10 (1998), 19-38. MR 1490136 |
| Reference:
|
[11] Skrzypczak L.: Heat and harmonic extensions for function spaces of Hardy-Sobolev-Besov type on symmetric spaces and Lie groups.J. Approx. Theory, to appear. Zbl 0918.43007, MR 1659396 |
| Reference:
|
[12] Strichartz R.S.: Analysis of the Laplacian on a complete Riemannian manifold.J. Funct. Anal. 52 (1983), 48-79. Zbl 0515.58037, MR 0705991 |
| Reference:
|
[13] Thangavelu S.: On Paley-Wiener theorems for the Heisenberg group.J. Funct. Anal. 115 (1993), 24-44. Zbl 0793.43006, MR 1228140 |
| Reference:
|
[14] Triebel H.: Function spaces on Lie Groups, the Riemannian approach.J. London Math. Soc. 35 (1987), 327-338. Zbl 0587.46036, MR 0881521 |
| Reference:
|
[15] Triebel H.: Theory of Function Spaces II.Birkhäuser Verlag, 1992. Zbl 0763.46025, MR 1163193 |
| Reference:
|
[16] Varopoulos N.Th., Saloff-Coste L., Coulhon T.: Analysis and Geometry on Groups.Cambridge Univ. Press, 1992. MR 1218884 |
| . |
