Abstract: | Let Γ be a simple closed curve that bounds the finite domain D , z =z (ζ )=z (r e i ? ) be the conformal mapping of the circle {ζ :|ζ |<1} onto the domain D . Furthermore, let the functions A (z ), B (z ) be given on D and U s ,2(A ;B ;D ) be the set of regular solutions of the equation . We call the Smirnov class E p (t )(A ;B ;D ) the set of those generalized functions W in D for which where p (t ) is a positive measurable function on Γ. We consider the Riemann‐Hilbert problem: Define a function W (z ) from the class E p (t )(A ;B ;D ) for which the equality, is fulfilled almost everywhere on Γ. It is assumed that Γ is a piecewise‐smooth curve without external peaks; , p is Log Hölder continuous and the function belongs to the class A (p (t );Γ), which is the generalization of the well‐known Simonenko class A (p ;Γ), where p is constant. The solvability conditions are established, and solutions are constructed. |