THE RIEMANN BOUNDARY VALUE PROBLEM IN VARIABLE EXPONENT SMIRNOV CLASS OF GENERALIZED ANALYTIC FUNCTIONS

The present paper studies the Riemann boundary value problem for generalized analytic in I. Vekua sense functions. The problem is formulated as follows: on the plane, cut along a simple, closed, rectifiable curve, find the generalized analytic function W (z) which in the domains G(+) and G(-), bounded by the curve, belongs to the Smirnov classes with a variable exponent and W+/- (t) its boundary values almost for all t is an element of Gamma satisfy the condition W+ (t) = a(t)W- (t) + b(t), where a(t) and b(t) are the given on functions. Various conditions of solvability are revealed and solutions (if any) are constructed.