Weighted Lp estimates of Kato square roots associated to degenerate elliptic operators
Yang, Dachun (Beijing Normal University. School of Mathematical Sciences)
Zhang, Junqiang (Beijing Normal University. School of Mathematical Sciences)

Date:	2017
Abstract:	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.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Kato square root ; Degenerate elliptic operator ; Riesz transform ; Lebesgue space ; Hardy space ; Square function ; Muckenhoupt weight
Published in:	Publicacions matemàtiques, Vol. 61 Núm. 2 (2017) , p. 395-444 (Articles) , ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/327586
DOI: 10.5565/PUBLMAT6121704

50 p, 812.9 KB

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