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Embeddings of shearlet coorbit spaces into Sobolev spaces. (English) Zbl 1511.22007

In applied mathematical analysis, shearlets are a multiscale framework which allows efficient encoding of anisotropic features in multivariate problem classes. Understanding how coefficient decay and smoothness of the analyzed signal are connected can be achieved using the theory of coorbit spaces.
In the present paper, the authors consider two families of shearlet dilation groups in dimension three and analyze how coorbit spaces associated to mixed \(L^p\)-spaces over these groups embed into Sobolev spaces.

MSC:

22D10 Unitary representations of locally compact groups
42B35 Function spaces arising in harmonic analysis
42C15 General harmonic expansions, frames
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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