On a Riemann boundary value problem in the space of p-summable functions with infinite index

Abstract

Abstract. The paper considers the Riemann boundary value problem in the half-plane in the space Lp(ρ), where weight function ρ(x) has infinite number of zeros. A necessary and sufficient condition is obtained for the normal solvability and Noetherianness of the considered problem. If the problem is solvable, solutions are represented in an explicit form.