Abstract: Solvability and regularity of the solution of the Dirichlet problem for the Prandtl equation (Formula presented.) is studied. Here p(x) is a positive function on (-1, 1) such that (Formula presented.). We introduce the scale of spaces (Formula presented.) in terms of the special integral transformation on the interval (-1, 1). We obtain theorems about the existence and uniqueness of the solution in the classes (Formula presented.) with (Formula presented.). In particular, for s = 1 the result is as follows: if (Formula presented.), then (Formula presented.), where (Formula presented.).