Conjugate harmonic Poisson integral for a half-plane and some of its approximation properties

Abstract

At present, the approximation properties of harmonic Poisson integrals for the upper half-plane, which satisfy the Laplace equation in Cartesian coordinates, have not been sufficiently studied. This paper studies the approximation properties of conjugate harmonic Poisson integrals for the upper half-plane on classes of Hölder functions. An exact equality is found for the upper bound of the deviation of the conjugate harmonic Poisson integral from its boundary value in a uniform metric.