The aim of this talk is to depict the general technique of F-transform
of functions of two variables on a background of a special Hilbert
space. Moreover, we extend the ordinary F-transform with constant
components to the F-transform of a higher degree (F^s-transform) with
s-degree polynomial components. The investigation of  this extension
indicates that by the F^s-transform components, we can approximate
not only the original function but also its partial derivatives.