Characterizations of GRS-weights, and consequences in time-frequency analysis

摘要

Let v be a submultiplicative weight. Then we prove that v satisfies Gel'fand-Raikov-Shilov-condition, if and only if v · e~(-ε|·|) is bounded for every positive ε. We use this equivalence to establish identification properties between weighted Lebesgue spaces, and between certain modulation spaces and Gelfand-Shilov spaces.