Average Width and Optimal Interpolation of the Sobolev-Wiener Class Wrpq(R) in the Metric Lq(R) Original Research Article

In this paper, we determine the exact value of average n − K width dn(Wrpq(R), Lq(R)) of Sobolev-Wiener class Wrpq(R) in the metric Lq(R) for 1 > q ≥ p > ∞ and get the value of dn(Wrp(R), Lqp(R)) for the dual case. We also solve the optimal interpolation problems of Wrpq(R) in the metric Lq(R) and Wrp(R) in the metric Lqp(R) for 1 < q ≤ p < ∞.