Intrinsic characterization and the extension operator in variable exponent function spaces on special Lipschitz domains
Intrinsic characterization and the extension operator in variable exponent function spaces on special Lipschitz domains
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DOI：
10.1007/978-981-10-6119-6_8
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发表时间：
2016-09
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影响因子：
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通讯作者：
Henning Kempka
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文献类型：
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作者：
Henning Kempka
本文研究了特殊Lipschitz域上具有变指数的2-微局部Besov和Triebel-Lizorkin空间。这类空间通常是由上相应空间的限制定义的，本文利用局部平均和Peetre极大算子给出了这类空间的两个内在刻画.此外，我们按照Rychkov在（J Lond Math Soc 60（1）：237-257，1999，[14]）中所做的方法构造了一个线性和有界的扩张算子，最后也证明了它是通用的。
We study 2-microlocal Besov and Triebel-Lizorkin spaces with variable exponents on special Lipschitz domains. These spaces are as usual defined by restriction of the corresponding spaces on. In this paper we give two intrinsic characterizations of these spaces using local means and the Peetre maximal operator. Further, we construct a linear and bounded extension operator following the approach done by Rychkov in (J Lond Math Soc 60(1):237–257, 1999, [14]), which at the end also turns out to be universal.