On a Riemann Boundary Value Problem in the Half-plane in the Class of Weighted Continuous Functions

摘要

Let C(.) be the class of functions f such that f(x).(x) is continuous on (-8,+8). In the upper half- plane of complex plane z we consider the Riemann boundary value problem in the weighted space C(.) with.(x) = m k= 1 x- xk x+ i ak, where ak and xk are real numbers, k = 1, 2,..., m. The problem is to determine an analytic in the upper and lower half- planes function F(z) to satisfy lim y.+ 0 F+(x + iy) - a(x) F -(x - iy) - f(x) C(.) = 0, where f. C(.), a(x). Cd[- A; A] for any A 0, a(x) = 0, the limit lim | x|.8 a(x) = a(8) exists and | a(x) - a(8)| C| x|- d for | x| = A 0. The normal solvability of this problem is established.