Conditions for subharmonicity and subharmonic extensions of functions

A. V. Pokrovskii

Sbornik. Mathematics, Tome 208 (2017) no. 8, pp. 1225-1245

Résumé

It is shown that the well-known local Blaschke-Privalov condition, which distinguishes the subharmonic functions in the set of real upper semicontinuous functions in a fixed Euclidean domain $G$ in terms of integral mean values over balls, can be replaced by other, a priori weaker, local conditions of this type on certain subsets of $G$. Both classical and new results on removable singularities of harmonic and subharmonic functions are obtained as consequences of the central theorem. Bibliography: 28 titles.

Détail

Keywords: subharmonic function, Blaschke-Privalov condition, inner Hausdorff measure, inner capacity, removable set.

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