Decay estimates on Besov and Triebel-Lizorkin spaces of the Stokes flows and the incompressible Navier-Stokes flows in half-spaces

Bui, The Anh; Bui, The Quan; Duong, Xuan Thinh

doi:10.1016/j.jde.2022.08.020

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Proof Of Theorem 161

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“…1,1 (R n ). See for example [6,Proposition 2.4]. In the setting of Theorem 5.1, we have a better estimates for the Riesz transform ∇ L −1/2 since by Theorem 3.13, Ḃ0…”

Section: Proof Of Theorem 16mentioning

confidence: 93%

New Atomic Decomposition for Besov Type Space $$\dot{B}^0_{1,1}$$ Associated with Schrödinger Type Operators

Bui

Duong

2023

J Fourier Anal Appl

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Let $$(X, d, \mu )$$ ( X , d , μ ) be a space of homogeneous type. Let L be a nonnegative self-adjoint operator on $$L^2(X)$$ L 2 ( X ) satisfying certain conditions on the heat kernel estimates which are motivated from the heat kernel of the Schrödinger operator on $$\mathbb {R}^n$$ R n . The main aim of this paper is to prove a new atomic decomposition for the Besov space $$\dot{B}^{0, L}_{1,1}(X)$$ B ˙ 1 , 1 0 , L ( X ) associated with the operator L. As a consequence, we prove the boundedness of the Riesz transform associated with L on the Besov space $$\dot{B}^{0, L}_{1,1}(X)$$ B ˙ 1 , 1 0 , L ( X ) .

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“…1,1 (R n ). See for example [6,Proposition 2.4]. In the setting of Theorem 5.1, we have a better estimates for the Riesz transform ∇ L −1/2 since by Theorem 3.13, Ḃ0…”

Section: Proof Of Theorem 16mentioning

confidence: 93%