Uehling potential and lowest-order corrections on vacuum polarization to the cross sections of some QED processes

Properties and different representations of the Uehling potential are investigated. Based on these properties by using our formulas for Fourier transform we have developed new analytical, logically closed physically transparent procedure which can be used to evaluate lowest-order vacuum polarization correction cross sections a number QED processes, including Mott electron scattering, bremsstrahlung, creation and/or annihilation $(e^{-}, e^{+})-$pair in field heavy Coulomb center, e.g., atomic nucleus.