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arXiv · 1209.6477

Bounded compositions on scaling invariant Besov spaces

Herbert Koch·Pekka Koskela·Eero Saksman·Tomás Soto
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Abstract

For $0 < s < 1 < q < \infty$, we characterize the homeomorphisms $\varphi : \real^n \to \real^n$ for which the composition operator $f \mapsto f \circ \varphi$ is bounded on the homogeneous, scaling invariant Besov space $\dot{B}^s_{n/s,q}(\real^n)$, where the emphasis is on the case $q\not=n/s$, left open in the previous literature. We also establish an analogous result for Besov-type function spaces on a wide class of metric measure spaces as well, and make some new remarks considering the scaling invariant Triebel-Lizorkin spaces $\dot{F}^s_{n/s,q}(\real^n)$ with $0 < s < 1$ and $0 < q \leq \infty$.

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Herbert Koch, Pekka Koskela, Eero Saksman, Tomás Soto. 2012-09-28. Bounded compositions on scaling invariant Besov spaces. https://arxiv.org/abs/1209.6477

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