Asymmetric approximations in the space L_p(t) - Litvin, E. G.; Polyakov, O. V. (Ukrains’kyi Matematychnyi Zhurnal, 1999)
We introduce the notion of (α,β)-norm in the space L_p(t) of functions x(t) for which _0^1 | x(t) |^p(t)< ∞ where p(t) is a positive measurable function. We establish a criterion for the element of the best (α,β)-approximation in the space L_p(t). We obtain inequalities of the type of duality relations.