The model of a non-uniform source of synchrotron radiation with a power-law radial distribution of the magnetic field and relativistic-electron density along one- or two-sided jets is described. Non-relativistic jets with both constant cross sections (collimated jets) and the cross sections that are proportional to distance (conical jets) are considered. Formulas that can be used to determine source parameters from the spectral index, source size, and index of the relativistic-electron energy spectrum based on multi-frequency observations are obtained. In the case of a conical jet, these formulas coincide with the analogous formulas for a spherical source obtained by A.P.Marscher. Relations that can be used to estimate the magnetic-field strength from the brightness temperature in the self-absorbed region are also obtained. As examples, the non-uniform source model is applied to the compact radio sources at the centers of the Milky Way, SgrA*, and the low-luminosity galactic nuclei M81* and M87*, which are associated with supermassive black holes. The inner radius of the radiation region is determined. For SgrA*, this distance turns out to be comparable to the gravitational radius, smaller than the radius of the last stable orbit for non-rotating black hole, and consistent with the radius of the last stable orbit expected for a rotating black hole. The inner radii in M81* and M87* are 15 RS, an order of magnitude larger then for SgrA*. Estimates of the magnetic field at the inner radius are 400 G for M81*, 0.65/5.3 kG for SgrA*, and 20/100 kG for M87*. These magnetic fields and the Blandford-Znajek model for the radiation of a rotating black hole are used to estimate the rotational speed of the black holes, which is in agreement with the characteristic variability time scales for these three objects. However, the accuracy of these estimates is modest, and is limited primarily by the accuracy of interferometric measurements at millimeter wavelengths.