GABOR ANALYSIS OF THE SPACES {\boldmath M( p, q,  w) ({Rd) AND S( p, q, r, w, ω) (Rd)

doi:10.1016/S0252-9602(11)60216-6

Abstract

Abstract:

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) ( R^d) to be the subspace of tempered distributions f ∈S´(R^d) such that the Gabor transform V_g(f) of f is in the weighted Lorentz space L( p, q, wdμ) (R^2d) . 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) (R^d) . Later we define the space S( p, q, r, w, ω)(R^d) 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) (R^d) . At the end of this article, we characterize the multipliers of
the spaces M( p, q, w) (R^d) and S( p, q, r, w, ω) ( R^d) .

Key words: Gabor transform, weigted Lorentz space, multiplier

CLC Number:

43A15

Ayse Sandikci A. Turan G¨urkanli. GABOR ANALYSIS OF THE SPACES {\boldmath M( p, q, w) ({R^d) AND S( p, q, r, w, ω) (R^d)[J].Acta mathematica scientia,Series B, 2011, 31(1): 141-158.

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GABOR ANALYSIS OF THE SPACES {\boldmath M( p, q, w) ({R^d) AND S( p, q, r, w, ω) (R^d)

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