Abstract
Let v be a submultiplicative weight. Then we prove that v satisfies Gel’fand–Raikov–Shilov-condition, if and only if \(v\cdot e^{-\varepsilon |\, \cdot \, |}\) is bounded for every positive \(\varepsilon \). We use this equivalence to establish identification properties between weighted Lebesgue spaces, and between certain modulation spaces and Gelfand–Shilov spaces.
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Acknowledgments
The research of the first two authors was partially supported by MEC and FEDER Project MTM2013-43540-P and GVA Prometeo II/2013/013.
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Fernández, C., Galbis, A. & Toft, J. Characterizations of GRS-weights, and consequences in time–frequency analysis. J. Pseudo-Differ. Oper. Appl. 6, 383–390 (2015). https://doi.org/10.1007/s11868-015-0122-z
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DOI: https://doi.org/10.1007/s11868-015-0122-z