부산대학교 도서관

Let m be a v-moderate function defined on R d and let g ∈ L 2( R d ). In this work, we defineΩ( R d ) to be the vector space of f ∈ L ( R d ) such that the Gabor transform V f belongs to L p ( R 2 d ), 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( R d ). We also discuss inclusion properties and obtain the dual space of Ω( R d ). At the end of this work, we study multipliers from L ( R d ) into Ω( R d ) and from Ω( R d ) into L ( R d ), where w is the Beurling weight function. [ABSTRACT FROM AUTHOR]