We introduce \(r\)-Fock space \(\mathscr{F}_{r}\) which generalizes some previously known Hilbert spaces, and study the \(r\)-derivative operator \(\frac{\mbox{d}^r}{\mbox{d}z^r}\) and the multiplication operator by \(z^r\). A general uncertainty inequality of Heisenberg-type is obtained. We also consider the extremal functions for the \(r\)-difference operator \(D_r\) on the space and obtain approximate inversion formulas.
