Let g be a non-zero rapidly decreasing function and w be a weight function. In this article in analog to modulation space, we define
the space M( p, q, w) ( Rd) to be the subspace of tempered distributions f ∈S´(Rd) such that the Gabor transform Vg(f) of f is in the weighted Lorentz space L( p, q, wdμ) (R2d) . We endow this space with a suitable norm and show that it becomes a Banach space and invariant under time frequence shifts for 1≤p, q≤∞. We also investigate the embeddings between these spaces and the dual space of M( p, q, w) (Rd) . Later we define the space S( p, q, r, w, ω)(Rd) for 1<p<∞, 1≤q ≤∞. We endow it with a sum norm and show that it becomes a Banach convolution algebra. We also discuss some properties of S( p, q, r, w, ω) (Rd) . At the end of this article, we characterize the multipliers of
the spaces M( p, q, w) (Rd) and S( p, q, r, w, ω) ( Rd) .
