Average Width and Optimal Interpolation of the Sobolev-Wiener Class Wpq(R) in the Metric Lq(R)

In this paper, we determine the exact value of average n − K width _n(W^r_pq(R), L_q(R)) of Sobolev-Wiener class W^r_pq(R) in the metric L_q(R) for 1 > q ≥ p > ∞ and get the value of _n(W^r_p(R), L_qp(R)) for the dual case. We also solve the optimal interpolation problems of W^r_pq(R) in the metric L_q(R) and W^r_p(R) in the metric L_qp(R) for 1 < q ≤ p < ∞.