The boundary Riemann problem of the power-logarithmic order of infinity index for the half-plane

Abstract

The boundary Riemann problem of the power-logarithmic order of infinity index for the half-plane in the class ℬ of bounded analytic functions and in the class ℬ₀(ρ, n) ⊂ ℬ, is investigated. Also, the necessary and sufficient conditions for the solution of this problem in the class ℬ₀(ρ, n), are obtained.