Let G be a noncompact connected Lie group, denote with ρ a right Haar measure and choose a family of linearly independent leftinvariant 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 Lpα(μχ) adapted to X and μ_χ (1<p<∞,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, Tommaso; Peloso, Marco M.; Tabacco, Anita; Vallarino, Maria. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - STAMPA. - 276:10(2019), pp. 3014-3050.
Titolo: | Sobolev spaces on Lie groups: Embedding theorems and algebra properties |
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Data di pubblicazione: | 2019 |
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Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.jfa.2018.11.014 |
Appare nelle tipologie: | 1.1 Articolo in rivista |
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http://hdl.handle.net/11583/2721540