Time-Frequency Analysis of Gabor Multipliers Associated with the Multidimensional Hankel-Stockwell Transform

The main crux of this paper is to introduce a new integral transform called the multidimensional Hankel-Stockwell transform and to give some new results related to this transform as generalized Parseval's, Plancherel's, inversion and Calderon's reproducing formulas. Next, we introduce a new pseudo-differential operator L psi 1,psi 2(sigma) related to this transform called Gabor multipliers which depend on a symbol sigma and two functions psi 1 and psi 2, we give a criteria in terms of the symbol sigma for its boundedness and compactness, we also show that this operator is a trace class operator and we give its trace formula.