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Eurasian Math. J., 2018, Volume 9, Number 3, Pages 85–94 (Mi emj307)  

Hardy spaces, approximation issues and boundary value problems

V. I. Vlasovab

a 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.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00781_
Ministry of Education and Science of the Russian Federation
This work was supported by Russian Foundation for Basic Research, proj. No. 16-01-0781 and RUDN University Program 5-100.


DOI: https://doi.org/10.32523/2077-9879-2018-9-3-85-94

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MSC: 34A55, 34B05, 58C40
Received: 01.02.2018
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Citation: V. I. Vlasov, “Hardy spaces, approximation issues and boundary value problems”, Eurasian Math. J., 9:3 (2018), 85–94

Citation in format AMSBIB
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\paper Hardy spaces, approximation issues and boundary value problems
\jour Eurasian Math. J.
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\vol 9
\issue 3
\pages 85--94
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