Continuous Characterizations of Besov-Lizorkin-Triebel Spaces and New Interpretations as Coorbits
Continuous Characterizations of Besov-Lizorkin-Triebel Spaces and New Interpretations as Coorbits
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DOI：
10.1155/2012/163213
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发表时间：
2010-07
影响因子：
--
通讯作者：
T. Ullrich
中科院分区：
文献类型：
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作者：
T. Ullrich
我们给出了齐次和非齐次Besov-Lizorkin-Triebel空间（H. Triebel 1983，1992，和2006）在连续的本地平均值的全部参数范围。特别地，我们证明了根据Feichtinger和Grochenig（H. G Feichtinger和K. Grochenig 1988，1989，and 1991）。这导致原子分解和小波基的齐性空间。特别是，我们给适当的小波矩，衰减和光滑条件的充分条件。
We give characterizations for homogeneous and inhomogeneous Besov-Lizorkin-Triebel spaces (H. Triebel 1983, 1992, and 2006) in terms of continuous local means for the full range of parameters. In particular, we prove characterizations in terms of Lusin functions (tent spaces) and spaces involving the Peetre maximal function to apply the classical coorbit space theory according to Feichtinger and Grochenig (H. G Feichtinger and K. Grochenig 1988, 1989, and 1991). This results in atomic decompositions and wavelet bases for homogeneous spaces. In particular we give sufficient conditions for suitable wavelets in terms of moment, decay and smoothness conditions.