A new characterization of the Riesz potential spaces with the aid of a composite wavelet transform
A new characterization of the Riesz potential spaces with the aid of a composite wavelet transform
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DOI：
10.1016/j.jmaa.2010.07.009
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发表时间：
2010-12
影响因子：
1.3
通讯作者：
Sinem Sezer;I. A. Aliev
中科院分区：
文献类型：
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作者：
Sinem Sezer;I. A. Aliev
我们引入了一个复合小波变换所产生的所谓的β-半群和小波测度。这种小波变换使人们能够获得一个新的显式反演公式的Riesz潜力和Riesz潜力空间的一个新的特征。使用的概念“β-半群”，这是一个自然的推广，著名的高斯-Weierstrass和泊松半群，使一个最小化的条件的数量小波测度，无论多大的顺序Riesz的潜力。
We introduce a composite wavelet-like transform generated by the so-called beta-semigroup and a wavelet measure. This wavelet-like transform enables one to obtain a new explicit inversion formula for the Riesz potentials and a new characterization of the Riesz potential spaces. The usage of the concept “beta-semigroup”, which is a natural generalization of the well-known Gauss–Weierstrass and Poisson semigroups, enables one to minimize the number of conditions on wavelet measure, no matter how big the order of Riesz's potentials is.