Spaces of Variable Smoothness and Integrability: Characterizations by Local Means and Ball Means of Differences
Spaces of Variable Smoothness and Integrability: Characterizations by Local Means and Ball Means of Differences
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DOI：
10.1007/s00041-012-9224-7
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发表时间：
2011-03
影响因子：
1.2
通讯作者：
Henning Kempka;J. Vybíral
中科院分区：
文献类型：
--
作者：
Henning Kempka;J. Vybíral
我们研究的空间和Besov和Triebel-Lizorkin型最近在阿尔梅达和Hästö（J. Funct。Anal. 258（5）：1628-2655，2010）和Diening等人（J. Funct. Anal. 256（6）：1731-1768，2009）。这两种尺度涵盖了许多经典的具有固定指数的空间以及可变光滑的函数空间和可变可积的函数空间。Anal. 258（5）：1628-2655，2010）和Diening等人（J. Funct. Anal. 256（6）：1731-1768，2009）通过傅立叶分析工具，作为单位的分解。令人惊讶的是，我们的主要结果表明，这些空间也允许在时域的特征与经典球手段的difference.To的帮助下，为此，我们首先证明了一个本地的手段特征与所谓的Peetre极大函数的帮助下。我们的结果也适用于2-微局部函数空间和2-微局部函数空间，它们是广义光滑空间和变光滑空间的轻微推广。
We study the spacesandof Besov and Triebel-Lizorkin type as introduced recently in Almeida and Hästö (J. Funct. Anal. 258(5):1628–2655, 2010) and Diening et al. (J. Funct. Anal. 256(6):1731–1768, 2009). Both scales cover many classical spaces with fixed exponents as well as function spaces of variable smoothness and function spaces of variable integrability.The spacesandhave been introduced in Almeida and Hästö (J. Funct. Anal. 258(5):1628–2655, 2010) and Diening et al. (J. Funct. Anal. 256(6):1731–1768, 2009) by Fourier analytical tools, as the decomposition of unity. Surprisingly, our main result states that these spaces also allow a characterization in the time-domain with the help of classical ball means of differences.To that end, we first prove a local means characterization forwith the help of the so-called Peetre maximal functions. Our results do also hold for 2-microlocal function spacesandwhich are a slight generalization of generalized smoothness spaces and spaces of variable smoothness.