This article is cited in 4 papers

Hardy spaces, approximation issues and boundary value problems

V. I. Vlasov<sup>ab

a</sup> RUDN University, 6 Mikluho-Malaya St, 117198 Moscow, Russia
^b Department of Applied Mathematical Physics, Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 40 Vavilova St, 113999 Moscow, Russia

Abstract: The weighted Hardy spaces $e_p(\mathscr{B};\rho)$ of harmonic functions are introduced on simply connected domains $\mathscr{B}$ 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 $e_p(\mathscr{B};\rho)$ are studied.

Keywords and phrases: Hardy spaces, analytic and harmonic functions, boundary value problem solvability, harmonic polynomials, approximation issues.

MSC: 34A55, 34B05, 58C40

Received: 01.02.2018

Language: English

DOI: 10.32523/2077-9879-2018-9-3-85-94

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