It in .shown that, the estimates for potentials obtained by Landkof are, in a sense, unimprovable. To prove this, we establish exact estimates for the Haus-dorlF men.suro and the capacity of Cantor sets in E, in 1, and estimates for potentials on these sets. These results are used in other sections of this article. FroHtman's theorem on the comparison of the Hausdorff measure with the capacity is supplemented with inequalities that connect the capacity and the girth in the sense of Hausdorff. We find an exact condition on measuring functions under which convergence of the integral Jo K(b)dh(l) is necessary for the validity of Prostman's theorem (here h is the measuring function and K is the kernel of the potential). The theorem of Govorov on the estimation of a subharmonic function in a disc (which, in turn, extends the Vniirou-Bernstein theorem on the lower estimation of the modulus of a holomorphic function) is generalized to 展开▼
