Let \(G\) be an affine group of elements \((x,y)\) such that \(y>0\), \(x\in\mathbb{R}\), with the group law \((x',y')(x,y)=(y'x+x',y'y)\), \(AAW\) be the space of admissible analyzing wavelets related to \(G\) with the Fourier transform supported in \([0,+\infty)\); \(\overline{AAW}=\{\psi\): \(\bar\psi\in AAW\}\); \(U=\{(x,y)\): \(x\in\mathbb{R}\), \(y>0\}\). \(L^{2,-2}(U)\) denotes the space of functions \(f(x,y)\), \((x,y)\in U\), for which the integral \(\| f\|_ 2^ 2=\int_ U| f(x,y)|^ 2 dx dy/y^ 2\) is finite. By using a decomposition of \(AAW\) and \(\overline{AAW}\) by Laguerre polynomials the authors decompose \(L^{2,- 2}(U)\) in direct orthogonal sums. In accordance with this decomposition they define Toeplitz type operators and Hankel type operators. The boundedness and membership in the Schatten-von Neumann class of these operators is studied.