Weighted Lp estimates of Kato square roots associated to degenerate elliptic operators

• Autores: Dachun Yang, Junqiang Zhang
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 61, Nº 2, 2017, págs. 395-444
• Idioma: inglés
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• Resumen

  • 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.