On Toeplitz-type Operators Related to Wavelets

Let G be the "ax+b"-group with the left invariant Haar measure d nu and psi be a fixed real-valued admissible wavelet on L(2)(R). The structure of the space of Calderon ( wavelet) transforms W(psi) (L(2)(R)) inside L(2)(G, d nu) is described. Using this result some representations, properties and the Wick calculus of the Calderon-Toeplitz operators T(a) acting on W(psi)(L(2)(R)) whose symbols a = a(zeta) depend on v = (sic)zeta for zeta is an element of G are investigated.