Inhomogeneous Hilbert boundary value problem with several points of logarithmic turbulence

We consider the so called Hilbert boundary value problem with boundary condition in the unit disk. Its coficient is assumed to be Hölder-continuous everywhere on the unit circle excluding a finite set of points. At these points its argument has nonremovable discontinuity of logarithmic order. We obtain formulas for the general solution and describe completely the solvability picture in a class of analytic and bounded functions in unit disc. Our technique is based on the theory of entire functions of zero-order approximation and the geometric theory of functions. The results obtained are applied to the study of the solvability of a single boundary value problem for a certain class generalized analytic function.