Pointwise Characterizations of Besov and Triebel-Lizorkin Spaces and Quasiconformal Mappings
Pointwise Characterizations of Besov and Triebel-Lizorkin Spaces and Quasiconformal Mappings
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DOI：
10.1016/j.aim.2010.10.020
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发表时间：
2010-04
期刊：
影响因子：
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通讯作者：
P. Koskela;Dachun Yang;Yuan Zhou
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文献类型：
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作者：
P. Koskela;Dachun Yang;Yuan Zhou
本文利用点态不等式刻画了度量测度空间中具有二重和反二重性质的经典Besov空间B stecp，q和Triebel-Lizorkin空间F stecp，q，其中s∈（0，1），p，q∈（n/（n+s），∞]都在R中.利用这一刻划，证明了拟共形映射对所有s∈（0，1）和q∈（n/（n+s），∞]保持F stecn/s，qson Rn.还建立了上述态射性质的度量测度空间形式。
In this paper, the authors characterize, in terms of pointwise inequalities, the classical Besov spaces B˙p,qsand Triebel–Lizorkin spaces F˙p,qsfor all s∈(0,1) and p,q∈(n/(n+s),∞], both in Rnand in the metric measure spaces enjoying the doubling and reverse doubling properties. Applying this characterization, the authors prove that quasiconformal mappings preserve F˙n/s,qson Rnfor all s∈(0,1) and q∈(n/(n+s),∞]. A metric measure space version of the above morphism property is also established.