Quasi-Compactness in Quasi-Banach Spaces

Lipschitz Structure of Quasi-banach Spaces

We show that the Lipschitz structure of a separable quasi-Banach space does not determine, in general, its linear structure. Using the notion of the Arens-Eells p-space over a metric space for 0 < p ≤ 1 we construct examples of separable quasi-Banach spaces which are Lipschitz isomorphic but not linearly isomorphic.

On quasi-complemented subspaces of banach spaces.

Coorbit Space Theory for Quasi-Banach Spaces

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 modul...

Wiener Amalgam Spaces with respect to Quasi-Banach Spaces

We generalize the theory of Wiener amalgam spaces on locally compact groups to quasi-Banach spaces. As a main result we provide convolution relations for such spaces. Also we weaken the technical assumption that the global component is invariant under right translations, which is even new for the classical Banach space case. To illustrate our theory we discuss in detail an example on the ax + b...

On the Quadratic Mapping in Generalized Quasi-banach Spaces

In this paper, we prove the Hyers–Ulam–Rassias stability of the quadratic mapping in generalized quasi-Banach spaces, and of the quadratic mapping in generalized p-Banach spaces.