Non-smooth atomic decomposition of 2-microlocal spaces and application to pointwise multipliers

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• 作者：Helena F. Gonç ; alves ^{helena.goncalves@mathematik.tu-chemnitz.de" class="auth_mail" title="E-mail the corresponding author} ; Henning Kempka ; ^{henning.kempka@mathematik.tu-chemnitz.de" class="auth_mail" title="E-mail the corresponding author}
• 关键词：2-microlocal spaces ; Besov and Triebel&ndash ; Lizorkin spaces ; Variable integrability ; Atomic decomposition ; Pointwise multipliers
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：15 February 2016
• 年：2016
• 卷：434
• 期：2
• 页码：1875-1890
• 全文大小：421 K

文摘

We provide non-smooth atomic characterizations for 2-microlocal Besov and Triebel–Lizorkin spaces with variable integrability $B_{p(\cdot ),q(\cdot )}^{\mathit{w}}({\mathbb{R}}^n)$ and $F_{p(\cdot ),q(\cdot )}^{\mathit{w}}({\mathbb{R}}^n)$. These spaces cover the classical Besov and Triebel–Lizorkin spaces as well as spaces of variable smoothness and integrability. As an application, we state a pointwise multipliers result for these spaces.