Abstract
Let m be a v-moderate function defined on R d and let g ∈ L 2(R d). In this work, we defineΩ p m (R d) to be the vector space of f ∈ L 2m (R d) such that the Gabor transform V f belongs to L p(R 2d), where 1 ≤ p < ∞. We equip it with a norm and show that it is a Banach space with this norm. We also study some preliminary properties of Ω p m (R d). We also discuss inclusion properties and obtain the dual space of Ω p m (R d). At the end of this work, we study multipliers from L 1w (R d) into Ω p w (R d) and from Ω p w (R d) into L ∞ w−1 (R d), where w is the Beurling weight function.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 1, pp. 139–145, January, 2006.
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Sandikçi, A., Gürkanli, A.T. The space Ω p m (R d) and some properties. Ukr Math J 58, 155–162 (2006). https://doi.org/10.1007/s11253-006-0058-9
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DOI: https://doi.org/10.1007/s11253-006-0058-9