The N-Widths of Hardy-Sobolev Spaces of Several Complex Variables

AbstractLet B denote the unit ball in Cn with boundary S and let σ(v) be the standard normalized measure on S(B). For fixed 1 ≤ p ≤ ∞, R≥ 1 let BHp(BR) (BAp(BR)) denote the unit ball of the Hardy space Hp (resp. the Bergman space Ap) in BR ≔ RB and for l ∈ N let HR(l, p, n) (resp. AR(l, p, n)) denote the class of those functions which have the lth radial derivative belonging to BHp(BR) (BAp(BR)) for l = 0, let HR(0, p, n) ≔ BHp(BR) (AR(0, p, n) ≔ BAp(BR)). The values of Kolmogorov, Gel′fand, and Bernstein and linear N-widths of classes HR(l, p, n) and AR(l, p, n) in the metrics Lp(σ) and Lp(v) (except for AR(l, p, n) in Lp(σ)) are found. For all 1≤ p, q ≤ ∞, R > 1 the asymptotic estimates of N-widths for classes HR(l, p, n) and AR(l, p, n) in the spaces Lq(σ) and Lq(v) are also obtained