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Article overview
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Bounded compositions on scaling invariant Besov spaces | Herbert Koch
; Pekka Koskela
; Eero Saksman
; Tomás Soto
; | Date: |
28 Sep 2012 | Abstract: | For $0 < s < 1 < q < infty$, we characterize the homeomorphisms $varphi :
{mathbb R}^n o {mathbb R}^n$ for which the composition operator $f mapsto
f circ varphi$ is bounded on the homogeneous, scaling invariant Besov space
$dot{B}^s_{n/s,q}({mathbb R}^n)$, where the emphasis is on the case
$q
ot=n/s$, 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-Lizorking spaces $dot{F}^s_{n/s,q}({mathbb R}^n)$ with $0 <
s < 1$ and $0 < q leq infty$. | Source: | arXiv, 1209.6477 | Services: | Forum | Review | PDF | Favorites |
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