# On operators satisfying the Rockland condition

Studia Mathematica (1998)

- Volume: 131, Issue: 1, page 63-71
- ISSN: 0039-3223

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topHebisch, Waldemar. "On operators satisfying the Rockland condition." Studia Mathematica 131.1 (1998): 63-71. <http://eudml.org/doc/216563>.

@article{Hebisch1998,

abstract = {Let G be a homogeneous Lie group. We prove that for every closed, homogeneous subset Γ of G* which is invariant under the coadjoint action, there exists a regular kernel P such that P goes to 0 in any representation from Γ and P satisfies the Rockland condition outside Γ. We prove a subelliptic estimate as an application.},

author = {Hebisch, Waldemar},

journal = {Studia Mathematica},

keywords = {Rockland condition; regular kernel; homogeneous Lie group; Schwartz class function; operator},

language = {eng},

number = {1},

pages = {63-71},

title = {On operators satisfying the Rockland condition},

url = {http://eudml.org/doc/216563},

volume = {131},

year = {1998},

}

TY - JOUR

AU - Hebisch, Waldemar

TI - On operators satisfying the Rockland condition

JO - Studia Mathematica

PY - 1998

VL - 131

IS - 1

SP - 63

EP - 71

AB - Let G be a homogeneous Lie group. We prove that for every closed, homogeneous subset Γ of G* which is invariant under the coadjoint action, there exists a regular kernel P such that P goes to 0 in any representation from Γ and P satisfies the Rockland condition outside Γ. We prove a subelliptic estimate as an application.

LA - eng

KW - Rockland condition; regular kernel; homogeneous Lie group; Schwartz class function; operator

UR - http://eudml.org/doc/216563

ER -

## References

top- [1] I. D. Brown, Dual topology of a nilpotent Lie group, Ann. Sci. École Norm. Sup. 6 (1973), 407-411. Zbl0284.57026
- [2] M. Christ, D. Geller, P. Głowacki and L. Pollin, Pseudodifferential operators on groups with dilations, Duke Math. J. 68 (1992), 31-65. Zbl0764.35120
- [3] R. Coifman et G. Weiss, Analyse Harmonique Non-Commutative sur Certains Espaces Homogènes, Lecture Notes in Math. 242, Springer, Berlin, 1971. Zbl0224.43006
- [4] R. Coifman et G. Weiss, Transference Methods in Analysis, CBMS Regional Conf. Ser. in Math. 31, Amer. Math. Soc., Providence, 1977. Zbl0371.43009
- [5] J. Dziuba/nski, A remark on a Marcinkiewicz-Hörmander multiplier theorem for some non-differential convolution operators, Colloq. Math. 58 (1989), 77-83. Zbl0711.43003
- [6] G. B. Folland and E. M. Stein, Hardy Spaces on Homogeneous Groups, Princeton Univ. Press, 1982. Zbl0508.42025
- [7] P. Głowacki, Stable semi-groups of measures as commutative approximate identities on non-graded homogeneous groups, Invent. Math. 83 (1986), 557-582. Zbl0595.43006
- [8] P. Głowacki, The inversion problem for singular integral operators on homogeneous groups, Studia Math. 87 (1987), 53-69. Zbl0646.47034
- [9] P. Głowacki, The Rockland condition for nondifferential convolution operators, Duke Math. J. 58 (1989), 371-395. Zbl0678.43002
- [10] P. Głowacki, The Rockland condition for nondifferential convolution operators II, Studia Math. 98 (1991), 99-114. Zbl0737.43002
- [11] B. Helffer et J. Nourrigat, Caractérisation des opérateurs hypoelliptiques homogènes invariants à gauche sur un groupe gradué, Comm. Partial Differential Equations 3 (1978), 889-958. Zbl0423.35040
- [12] A. Hulanicki and J. W. Jenkins, Nilpotent Lie groups and summability of eigenfunction expansions of Schrödinger operators, Studia Math. 80 (1984), 235-244. Zbl0564.43007
- [13] A. A. Kirillov, Unitary representations of nilpotent Lie groups, Uspekhi Mat. Nauk 17 (4) (1962), 57-110 (in Russian).
- [14] J. Nourrigat, Inégalités ${L}^{2}$ et représentations de groupes nilpotents, J. Funct. Anal. 74 (1987), 300-327. Zbl0644.35026
- [15] J. Nourrigat, ${L}^{2}$ inequalities and representations of nilpotent groups, C.I.M.P.A. School of Harmonic Analysis, Wuhan, to appear. Zbl0644.35026

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