Abstract
In the present paper, we present a natural extension of the modulation spaces M p , q s with 0 < p < ∞ , 0 < q ⩽ ∞ and s ∈ R . The weight we take up here belongs to the class A ∞ loc , which is even wider and contains weights of exponential growth. After defining the function spaces, we investigate their atomic and molecular decomposition as well as some elementary properties.
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