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Eurasian Math. J., 2018, Volume 9, Number 4, Pages 9–21 (Mi emj309)  

On the Dirichlet problem for the Laplace equation with the boundary value in Morrey space

N. R. Ahmedzade, Z. A. Kasumov

Institute of Mathematics and Mechanics of NAS of Azerbaijan, 9 B. Vahabzade St., AZ1141, Baku, Azerbaijan

Abstract: The class of Poisson–Morrey harmonic functions in the unit circle is introduced, some properties of functions of this class are studied. Nontangential maximal function is considered and it is estimated from above via maximum operator, and the proof is carried out for the Poisson–Stieltjes integral, when the density belongs to the corresponding Morrey–Lebesgue space. The obtained results are applied to solving of the Dirichlet problem for the Laplace equation with the boundary value in Morrey–Lebesgue space.

Keywords and phrases: Morrey–Poisson class, maximal function, Morrey–Lebesgue space.

DOI: https://doi.org/10.32523/2077-9879-2018-9-4-9-21

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Document Type: Article
MSC: 30E25, 46E30
Received: 20.02.2017
Revised: 06.11.2018
Language: English

Citation: N. R. Ahmedzade, Z. A. Kasumov, “On the Dirichlet problem for the Laplace equation with the boundary value in Morrey space”, Eurasian Math. J., 9:4 (2018), 9–21

Citation in format AMSBIB
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\by N.~R.~Ahmedzade, Z.~A.~Kasumov
\paper On the Dirichlet problem for the Laplace equation with the boundary value in Morrey space
\jour Eurasian Math. J.
\yr 2018
\vol 9
\issue 4
\pages 9--21
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\crossref{https://doi.org/10.32523/2077-9879-2018-9-4-9-21}
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