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′...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）.展开更多
文摘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）.
