Hardy spaces, approximation issues and boundary value problems

Abstract

The weighted Hardy spaces e_p(𝔏; ρ) of harmonic functions are introduced on simply connected domains 𝔏 with rectifiable boundaries. Boundary properties of functions in these spaces are investigated, the solvability of the Dirichlet problem is established, while its solution with its derivatives are estimated. Approximation properties of the system of harmonic polynomials in e_p(𝔏; ρ) are studied.