Acta mathematica scientia, Series B >
GABOR ANALYSIS OF THE SPACES {\boldmath M( p, q, w) ({Rd) AND S( p, q, r, w, ω) (Rd)
Received date: 2007-09-17
Revised date: 2008-12-25
Online published: 2011-01-20
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) .
Key words： Gabor transform; weigted Lorentz space; multiplier
Ayse Sandikci A. Turan G¨urkanli . GABOR ANALYSIS OF THE SPACES {\boldmath M( p, q, w) ({Rd) AND S( p, q, r, w, ω) (Rd)[J]. Acta mathematica scientia, Series B, 2011 , 31(1) : 141 -158 . DOI: 10.1016/S0252-9602(11)60216-6
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