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arXiv · 1609.02345

Intrinsic characterization and the extension operator in variable exponent function spaces on special Lipschitz domains

Henning Kempka
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Abstract

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 $\R^n$. 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, which at the end also turns out to be universal.

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Henning Kempka. 2016-09-08. Intrinsic characterization and the extension operator in variable exponent function spaces on special Lipschitz domains. https://arxiv.org/abs/1609.02345

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