The space $\Omega^p_m(R^d)$ and some properties
Let $m$ be a $v$-moderate function defined on $R^d$ and let $g \in L^2(R^d)$. In this work, we define $\Omega ^p_m(R^d)$ to be the vector space of $f \in L^2_n(R^d)$ such that the Gabor transform $V_gf$ belongs to $L^p(R^{2d})$, where $1 \leq p < \infty$. We endowe it with a norm and show tha...
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| Datum: | 2006 |
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| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2006
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/3441 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | Let $m$ be a $v$-moderate function defined on $R^d$ and let $g \in L^2(R^d)$. In this work, we define $\Omega ^p_m(R^d)$ to be the vector space of $f \in L^2_n(R^d)$ such that the Gabor transform $V_gf$ belongs to $L^p(R^{2d})$, where $1 \leq p < \infty$. We endowe it with a norm and show that it is a Banach space with this norm.
We also study some preliminary properties of $\Omega ^p_m(R^d)$.
Later we discuss inclusion properties and obtain the dual space of $\Omega ^p_m(R^d)$. At the end of this work, we study multipliers from $L_w^1 (R^d)$
into $\Omega ^p_w(R^d)$ and from $\Omega ^p_w(R^d)$ into $L^{\infty}_{w^{-1}}(R^d)$, where $w$
is Beurling's weight function. |
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