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...

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Detalles Bibliográficos
Autores: Yang, Dachun, Zhang, Junqiang
Tipo de recurso: artículo
Fecha de publicación:2017
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:180445
Acceso en línea:https://ddd.uab.cat/record/180445
https://dx.doi.org/urn:doi:10.5565/PUBLMAT6121704
Access Level:acceso abierto
Palabra clave:Kato square root
Degenerate elliptic operator
Riesz transform
Lebesgue space
Hardy space
Square function
Muckenhoupt weight
Descripción
Sumario: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.