Weighted Lp estimates of Kato square roots associated to degenerate elliptic operators
Let w be a Muckenhoupt A2(Rn) weight and Lw := -w-1 div(A∇) the degenerate elliptic operator on the Euclidean space Rn, n ≥ 2. In this article, the authors establish some weighted Lp estimates of Kato square roots associated to the degenerate elliptic operators Lw. More precisely, the authors prove...
| Autores: | , |
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| Formato: | artículo |
| Fecha de publicación: | 2017 |
| País: | España |
| Recursos: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:180445 |
| Acesso em linha: | https://ddd.uab.cat/record/180445 https://dx.doi.org/urn:doi:10.5565/PUBLMAT6121704 |
| Access Level: | acceso abierto |
| Palavra-chave: | Kato square root Degenerate elliptic operator Riesz transform Lebesgue space Hardy space Square function Muckenhoupt weight |
| Resumo: | Let w be a Muckenhoupt A2(Rn) weight and Lw := -w-1 div(A∇) the degenerate elliptic operator on the Euclidean space Rn, n ≥ 2. In this article, the authors establish some weighted Lp estimates of Kato square roots associated to the degenerate elliptic operators Lw. More precisely, the authors prove that, for w ∈ Ap(Rn), p ∈ (2n n+1 , 2] and any f ∈ C∞c (Rn), kL 1/2 w (f)kLp(w,Rn) ∼ k∇fkLp(w,Rn), where C∞c (Rn) denotes the set of all infinitely differential functions with compact supports and the implicit equivalent positive constants are independent of f. |
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