Criteria of the removable sets for the weighted spaces of harmonic functions. (English. Russian original) Zbl 1081.31004

Demshin, I. N.; Shlyk, V. A.

J. Math. Sci., New York 122, No. 6, 3616-3622 (2004); translation from Zap. Nauchn. Semin. POMI 286, 62-73 (2002).

The authors continue the investigations of L. I. Hedberg [Ark. Math. 12, 181–201 (1974; Zbl 0297.30017)] on the theory of removable sets for the weighted spaces \(L^1_{p,\omega}\) of harmonic functions and obtain several new criteria.

Reviewer: Yusuf Avci (Ýstanbul)

MSC:

31B05	Harmonic, subharmonic, superharmonic functions in higher dimensions
31B15	Potentials and capacities, extremal length and related notions in higher dimensions

Keywords:

sharp functional; capacity; Muckenhoupt’s weight; removable sets

Citations:

Zbl 0297.30017