Wiener amalgam spaces with respect to quasi-Banach spaces
Volume 109 / 2007
Colloquium Mathematicum 109 (2007), 345-362 MSC: 46A16, 46E27, 46E30. DOI: 10.4064/cm109-2-13
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 new even for the classical Banach space case. To illustrate our theory we discuss in detail an example on the $ax+b$ group.