Let G be a noncompact connected Lie group, denote with ρ a right Haar measure and choose a family of linearly independent left-invariant vector fields X on G satisfying Hörmander's condition. Let χ be a positive character of G and consider the measure μ χ whose density with respect to ρ is χ. In this paper, we introduce Sobolev spaces L αp (μ χ ) adapted to X and μ χ (1<∞ α≥0) and study embedding theorems and algebra properties of these spaces. As an application, we prove local well-posedness and regularity results of solutions of some nonlinear heat and Schrödinger equations on the group.

Sobolev spaces on Lie groups: Embedding theorems and algebra properties

Bruno T.;
2019-01-01

Abstract

Let G be a noncompact connected Lie group, denote with ρ a right Haar measure and choose a family of linearly independent left-invariant vector fields X on G satisfying Hörmander's condition. Let χ be a positive character of G and consider the measure μ χ whose density with respect to ρ is χ. In this paper, we introduce Sobolev spaces L αp (μ χ ) adapted to X and μ χ (1<∞ α≥0) and study embedding theorems and algebra properties of these spaces. As an application, we prove local well-posedness and regularity results of solutions of some nonlinear heat and Schrödinger equations on the group.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11567/1092877
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