Abstract
We introduce the notion of the (k, a)-generalized wavelet multipliers. Particular cases of such generalized wavelet multipliers are the classical and Dunkl wavelet multipliers. The restriction of the (k, a)-generalized wavelet multipliers to radial functions is given by the generalized Hankel wavelet multiplier. We study the boundedness, Schatten class properties of the (k, a)-generalized wavelet multipliers and we give them trace formula. We prove that the generalized Landau-Pollak-Slepian operator is a (k, a)-generalized wavelet multiplier. Next, we give results on the boundedness and compactness of (k, a)-generalized wavelet multipliers on L-k, a(p) (R-d), 1 <= p <= infinity.