Convolution and Wiener Amalgam Spaces on the Affine Group

Wiener amalgam spaces are a class of spaces of functions or distributions defined by a norm which amalgamates a local criterion for membership in the space with a global criterion. Versions of such amalgam spaces have arisen independently many times in the literature, and often provide a natural and compelling context for formulating results. As one illustration of the shortcomings of the usual Lebesgue space L(R) in regard to distinguishing between local and global properties of functions, note that all rearrangements of a function have identical L norms. Hence it is not possible to recognize from its norm whether a function is the characteristic