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1996 | 69 | 1 | 29-36
Tytuł artykułu

Multiplier theorem on generalized Heisenberg groups II

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We prove that on a product of generalized Heisenberg groups, a Hörmander type multiplier theorem for Rockland operators is true with the critical index n/2 + ϵ, ϵ>0, where n is the euclidean (topological) dimension of the group.
Słowa kluczowe
Rocznik
Tom
69
Numer
1
Strony
29-36
Opis fizyczny
Daty
wydano
1996
otrzymano
1993-12-13
poprawiono
1994-05-16
Twórcy
  • Institute of Mathematics, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
  • Institute of Mathematics, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
Bibliografia
  • [1] M. Christ, $L^p$ bound for spectral multiplier on nilpotent groups, Trans. Amer. Math. Soc. 328 (1991), 73-81.
  • [2] J. Cygan, Heat kernels for class 2 nilpotent groups, Studia Math. 64 (1979), 227-238.
  • [3] J. Dziubański, A remark on a Marcinkiewicz-Hörmander multiplier theorem for some non-differential convolution operators, Colloq. Math. 58 (1989), 77-83.
  • [4] G. B. Folland and E. M. Stein, Hardy Spaces on Homogeneous Groups, Princeton Univ. Press, 1982.
  • [5] B. Gaveau, Principe de moindre action, propagation de la chaleur et estimées sous-elliptiques sur certains groupes nilpotents, Acta Math. 139 (1977), 95-153.
  • [6] P. Głowacki, The Rockland condition for nondifferential convolution operators, Duke Math. J. 58 (1989), 371-395.
  • [7] W. Hebisch, A multiplier theorem for Schrödinger operators, Colloq. Math. 60/61 (1990), 659-664.
  • [8] W. Hebisch, Almost everywhere summability of eigenfunction expansions associated to elliptic operators, Studia Math. 96 (1990), 263-275.
  • [9] W. Hebisch, Multiplier theorem on generalized Heisenberg groups, Colloq. Math. 65 (1993), 231-239.
  • [10] W. Hebisch and A. Sikora, A smooth subadditive homogeneous norm on a homogeneous group, Studia Math. 96 (1990), 231-236.
  • [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.
  • [12] A. Hulanicki, Subalgebra of $L_1(G)$ associated with laplacian on a Lie group, Colloq. Math. 31 (1974), 259-287.
  • [13] A. Hulanicki, The distribution of energy in the Brownian motion in the Gaussian field and analytic-hypoellipticity of certain subelliptic operators on the Heisenberg group, Studia Math. 56 (1976), 165-179.
  • [14] A. Hulanicki and J. W. Jenkins, Nilpotent Lie groups and summability of eigenfunction expansions of Schrödinger operators, ibid. 80 (1984), 235-244.
  • [15] G. Mauceri and S. Meda, Vector-valued multipliers on stratified groups, Rev. Mat. Iberoamericana 3-4 (6) (1990), 141-154.
  • [16] D. Müller and E. M. Stein, On spectral multipliers for Heisenberg and related groups, J. Math. Pures Appl., to appear.
  • [17] J. Randall, The heat kernel for generalized Heisenberg groups, to appear.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-cmv69i1p29bwm
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