Removable singularities for 𝐻^{𝑝}-functions

Järvi, Pentti

doi:10.1090/S0002-9939-1982-0674087-4

Removable singularities for $H^{p}$-functions
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Proc. Amer. Math. Soc. 86 (1982), 596-598 Request permission

Abstract:

Given a domain $D$ in ${{\mathbf {C}}^n}$, a holomorphic function $f$ on $D$ is said to belong to ${H^p}(D)$, $0 < p < \infty$, provided that $| f |^p$ admits a harmonic majorant in $D$. In this note it is shown that ${H^p}(D\backslash E) = {H^p}(D)$ whenever $E$ is a relatively closed polar subset of $D$.

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