论文信息 - Estimates on the semigroups generated by left invariant operators on Lie groups.

Estimates on the semigroups generated by left invariant operators on Lie groups.

L is a well defined operator on D'(G). L is dissipative on Cc°° in L (G) so it can be extended to a generator of a semigroup of operators. In the case nj = l and XQ = 0 the semigroup has been studied by many authors e.g. D.S. Jerison and A.Sanehez-Calle [7] proved the upper and lower bound for its kernels when G is a homogeneous group (or a compact manifold). In a series of papers cf. [11] and the references there, N. Varopoulos studied these kernels on an arbitrary unimodular Lie group. The case X0 = 0 and G is homogeneous has been studied in [2], [3] and [4].

Waldemar Hebisch | W. Hebisch

[1] E. Stein,et al. Hypoelliptic differential operators and nilpotent groups , 1976 .

[2] A. Hulanicki. Subalgebra of $L_1(G)$ associated with Laplacian on a Lie group , 1974 .

[3] Bernard Helffer,et al. Caracterisation des operateurs hypoelliptiques homogenes , 1979 .

[4] Jacek Dziubański,et al. On semigroups generated by left-invariant positive differential operators on nilpotent Lie groups , 1989 .

[5] Waldemar Hebisch. Sharp pointwise estimate for the kernels of the semigroup generated by sums of even powers of vector fields on homogeneous groups , 1989 .