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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.

Criteria for weak compactness of vector-valued integration maps

Susumu Okada, Werner J. Ricker (1994)

Commentationes Mathematicae Universitatis Carolinae

Criteria are given for determining the weak compactness, or otherwise, of the integration map associated with a vector measure. For instance, the space of integrable functions of a weakly compact integration map is necessarily normable for the mean convergence topology. Results are presented which relate weak compactness of the integration map with the property of being a bicontinuous isomorphism onto its range. Finally, a detailed description is given of the compactness properties for the integration...

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