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Coorbit space theory for quasi-Banach spaces

Holger Rauhut (2007)

Studia Mathematica

We generalize the classical coorbit space theory developed by Feichtinger and Gröchenig to quasi-Banach spaces. As a main result we provide atomic decompositions for coorbit spaces defined with respect to quasi-Banach spaces. These atomic decompositions are used to prove fast convergence rates of best n-term approximation schemes. We apply the abstract theory to time-frequency analysis of modulation spaces M m p , q , 0 < p,q ≤ ∞.

Copies of lp in tensor products.

Fernando Blasco (2000)

Extracta Mathematicae

The problem of finding complemented copies of lp in another space is a classical problem in Functional Analysis and has been studied from different points of view in the literature. Here we pay attention to complementation of lp in an n-fold tensor product of lq spaces because we were lead to that result in the study of Grothendieck's Problème des topologies as we shall comment later.

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