The functions on the lattice generated by the integer degrees of q 2 are considered, 0< q<1. The q 2-shift operator is defined. The multiplicators and the q 2-convolutors are defined in the functional spaces which are dual with respect to the q 2-Fourier transform. The q 2-analog of convolution of two q 2-distributions is constructed. The q 2-analog of an arbitrary order derivative is introduced.