General Coorbit Space Theory for Quasi-Banach Spaces and Inhomogeneous Function Spaces with Variable Smoothness and Integrability
General Coorbit Space Theory for Quasi-Banach Spaces and Inhomogeneous Function Spaces with Variable Smoothness and Integrability
复制标题
DOI：
10.1007/s00041-016-9505-7
复制
发表时间：
2015-06
影响因子：
1.2
通讯作者：
Henning Kempka;M. Schäfer;T. Ullrich
中科院分区：
文献类型：
--
作者：
Henning Kempka;M. Schäfer;T. Ullrich
在这篇文章中，我们提出了一个一般的共轨空间理论，它适用于用一个由局部紧的Hausdorff空间标号的抽象连续框架和一个相关的广义语音变换来定义拟Banach空间的共轨。该理论实现了由Feichtinger和Gröchenig在20世纪80年代末提出的面向各种功能空间及其原子分解的普遍抽象理论的进一步发展。我们结合了Rauhut和Ullrich(J Funct anal260(11)：3299-3362,2011)和Rauhut(Stud Math 180(3)：237-253,2007)中的最新方法，特别地识别了各种Besov-Lizorkin-Triebel类型的非齐次(拟Banach)空间。为了证明我们的新理论的潜力，我们将其应用于具有可变光滑性和可积性的空间，这些空间在过去10年中引起了极大的兴趣。从抽象的离散化机制出发，我们得到了这些空间的原子分解和小波框架同构。
In this paper we propose a general coorbit space theory suitable to define coorbits of quasi-Banach spaces using an abstract continuous frame, indexed by a locally compact Hausdorff space, and an associated generalized voice transform. The proposed theory realizes a further step in the development of a universal abstract theory towards various function spaces and their atomic decompositions which has been initiated by Feichtinger and Gröchenig in the late 1980s. We combine the recent approaches in Rauhut and Ullrich (J Funct Anal 260(11):3299–3362, 2011) and Rauhut (Stud Math 180(3):237–253, 2007) to identify, in particular, various inhomogeneous (quasi-Banach) spaces of Besov–Lizorkin–Triebel type. To prove the potential of our new theory we apply it to spaces with variable smoothness and integrability which have attracted significant interest in the last 10 years. From the abstract discretization machinery we obtain atomic decompositions as well as wavelet frame isomorphisms for these spaces.