Removable singularities of subharmonic functions from \(L^2_p\) (Q2742998)
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scientific article; zbMATH DE number 1651013
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Removable singularities of subharmonic functions from \(L^2_p\) |
scientific article; zbMATH DE number 1651013 |
Statements
24 September 2001
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removable singularities
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subharmonic function
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Sobolev space
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Lebesgue measure
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JFM 60.1134.02
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Removable singularities of subharmonic functions from \(L^2_p\) (English)
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Removable singularities of subharmonic functions [see \textit{M. Brelot}, Étude des fonctions sousharmoniques au voisinage d'un point (Herman, 1934; Zbl 0009.01902)] from the Sobolev space \(L^2_p\) are studied. Let \(E\) be a compact set from the domain \(G\subset\mathbb R^n\). It is proved that \(E\) is a removable set for all subharmonic functions \(u(x)\) defined in \(G\backslash E\) and belonging to \(L^2_p(G)\) (\(p\geq 1\)), if and only if the Lebesgue measure of \(E\) is equal to zero.
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