Multiplier theorem on generalized Heisenberg groups

Waldemar Hebisch

ArticleOriginal scientific text

Title

Multiplier theorem on generalized Heisenberg groups

Authors ¹

Affiliations

Institute of Mathematics, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

M. Christ, $L^{p}$ bounds for spectral multipliers on nilpotent groups, Trans. Amer. Math. Soc. 328 (1991), 73-81.
J. Cygan, Heat kernels for class 2 nilpotent groups, Studia Math. 64 (1979), 227-238.
G. B. Folland and E. M. Stein, Hardy Spaces on Homogeneous Groups, Princeton University Press, 1982.
B. Gaveau, Principe de moindre action, propagation de la chaleur et estimations sous-elliptiques sur certains groupes nilpotents, Acta Math. 139 (1977), 95-153.
W. Hebisch, A multiplier theorem for Schrödinger operators, Colloq. Math. 60/61 (1990), 659-664.
--, Almost everywhere summability of eigenfunction expansions associated to elliptic operators, Studia Math. 96 (1990), 263-275.
A. Hulanicki, Subalgebra of $L_{1} (G)$ associated with laplacian on a Lie group, Colloq. Math. 31 (1974), 259-287.
--, 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), 165-173.
A. Hulanicki and J. W. Jenkins, Nilpotent Lie groups and summability of eigenfunction expansions of Schrödinger operators, ibid. 80 (1984), 235-244.
G. Mauceri and S. Meda, Vector-valued multipliers on stratified groups, Rev. Mat. Iberoamericana 6 (1990), 141-154.
H. P. McKean, -Δ plus a bad potential, J. Math. Phys. 18 (1977), 1277-1279.
D. Müller and E. M. Stein, On spectral multipliers for Heisenberg and related groups, J. Math. Pures Appl., to appear.
J. Randall, The heat kernel for generalized Heisenberg groups, to appear.

Title

Multiplier theorem on generalized Heisenberg groups

Affiliations

Bibliography