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We consider the heat kernel $ϕ_{t}$ corresponding to the left invariant sub-Laplacian with drift term in the first commutator of the Lie algebra, on a nilpotent Lie group. We improve the results obtained by G. Alexopoulos in [1], [2] proving the “exact Gaussian factor” exp(-|g|²/4(1+ε)t) in the large time upper Gaussian estimate for $ϕ_{t}$ . We also obtain a large time lower Gaussian estimate for $ϕ_{t}$ .

Sub-Laplacians of holomorphic $L^{p}$ -type on exponential Lie groups

Detlef Müller (2002)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In this survey article, I shall give an overview on some recent developments concerning the $L^{p}$ -functional calculus for sub-Laplacians on exponential solvable Lie groups. In particular, I shall give an outline on some recent joint work with W. Hebisch and J. Ludwig on sub-Laplacians which are of holomorphic $L^{p}$ -type, in the sense that every $L^{p}$ -spectral multiplier for $p \neq 2$ will be holomorphic in some domain.

The symbol calculus on the upper half plane is studied from the viewpoint of the Kirillov theory of orbits. The main result is the $L^{p}$ -estimates for Fuchs type pseudodifferential operators.

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Spherical functions on a complex classical quantum group

Spherical Functions on a Simply Connected Semisimple Lie Group. II. The Paley-Wiener Theorem for the Rank one Case.

Stability of mappings with bounded distortion in the Sobolev norm on the John domains of Heisenberg groups.

Stability of mappings with bounded distortion on a Heisenberg group.

Stable semi-groups of measures as commutative approximate identities on non-graded homogeneous groups.

Sub-Laplacian with drift in nilpotent Lie groups

Sub-Laplacians of holomorphic $L^{p}$ -type on exponential Lie groups

Sur la résolubilité locale des opérateurs bi-invariants

Sur la transformation de Radon de la sphère $S^{d}$

Sur les équations invariantes par un groupe

Sur les représentations différentiables des groupes de Lie algébriques

Sur les représentations induites des groupes de Lie

Sur les transformées de Riesz sur les espaces homogènes des groupes de Lie semi-simples

Symbol calculus on the affine group "ax + b"

Symmetry and nonsymmetry for a class of exponential Lie groups.

Symplectic convexity theorems and coadjoint orbits

Szegö Kernels Associated with Discrete Series.

Currently displaying 21 – 37 of 37