G. Khuskivadze and V. Paatashvili

On a Property of Harmonic Functions from the Smirnov Class

abstract:
It is proved that for harmonic functions from the Smirnov class $e(L_{1p}(\rho_1),L_{2q}'(\rho_2))$ (i.e., for functions satisfying the inequality (2)) in a simply connected domain with the Lyapunov boundary $L$ almost everywhere on $L$ there exist the angular boundary values which on the part $L_2$ of the boundary form an absolutely continuous function.

Mathematics Subject Classification: 31A05, 35J05

Key words and phrases: Harmonic functions, Smirnov classes of harmonic functions, Zaremba's problem, absolute continuity