Pointwise Characterizations of Besov and Triebel-Lizorkin Spaces and Quasiconformal Mappings
By Pekka Koskela, Dachun Yang, Yuan Zhou. 2010
153 citations recorded by the source corpus.
In this paper, the authors characterize, in terms of pointwise inequalities, the classical Besov spaces $\dot B^s_{p,\,q}$ and Triebel-Lizorkin spaces $\dot F^s_{p,\,q}$ for all $s\in(0,\,1)$ and $p,\,q\in(n/(n+s),\,\infty],$ both in ${\mathbb R}^n$ and in the metric measure spaces enjoying the doubling and reverse doubling properties. Applying this characterization, the authors prove that quasiconformal mappings preserve $\dot F^s_{n/s,\,q}$ on $\rn$ for all $s\in(0,\,1)$ and $q\in(n/(n+s),\,\infty]$. A metric measure space version of the above morphism property is also established.
Subfields: Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/d26508db2ebe0a2fbe5bddb39f5e923038800977
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In Applied Mathematics
- Yuan Zhou
- Dachun Yang
- Pekka Koskela
- L. Ihnatsyeva
- T. Heikkinen
- Liguang Liu
- Heli Tuominen
- Diego Maldonado
Citations in the corpus
- Multilinear analysis on metric spaces (2014, background): “RD-spaces have become the underlying context in numerous areas of analysis and PDEs, we refer the reader to [22, 23], [60, 61, 86], [71, 72, 40], [107, 109, 108] and references therein.”
- Measure Density and Extension of Besov and Triebel–Lizorkin Functions (2014, methodology): “In this paper, we mainly use the approach based on pointwise inequalities, introduced in [27].”
- Characterizations of Besov and Triebel–Lizorkin spaces on metric measure spaces (2011, background): “doubling and a reverse doubling property was established in [21] by Müller and Yang and the pointwise characterization of Ḃs p, q(X ) in [19].”
- Fractional Sobolev extension and imbedding (2014, background): “The second conclusion (2.6) was essentially proved in [10, (2.4)] (see also [20, (5.9)]).”
- Besov regularity for solutions of p-harmonic equations (2017, unknown): “The following result was proven in [15].”
- Fractional Differentiability for Solutions of Nonlinear Elliptic Equations (2016, background): “3 says that A ∈ Fn α ,∞ (see [17] for details).”
- Higher differentiability for solutions to a class of obstacle problems (2018, unknown): “The following result was proved in [30].”