The space ?mp(Rd) and some properties

Abstract

Let m be a v-moderate function defined on R d and let g L 2(R d ). In this work, we define? m p (R d ) to be the vector space of f L m 2 (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 ? m p (R d ). We also discuss inclusion properties and obtain the dual space of ? m p (R d ). At the end of this work, we study multipliers from L w 1 (R d ) into ? w p (R d ) and from ? w p (R d ) into L w-1 ? (R d ), where w is the Beurling weight function. © 2006 Springer Science+Business Media, Inc.