The space $\Omega^p_m(R^d)$ and some properties

• Date: 2006
• Main Authors: Gürkanli, A. T., Sandikçi, A., Гурканлі, А. Т., Сандикчи, А.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2006
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3441
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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...