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

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