n-Widths of Hp-spaces in Lq(−1, 1)

AbstractThe Kolmogorov n-widths dn, Gel'fand n-widths dn, and linear n-widths δn of the Hardy spaces Hp in Lq(−1, 1) are estimated. It is shown that for 1≤q<p≤∞ there exist constants k1, k2 such that k1n(12)(1p−1p)exp(−πn2(1q−1p)) ≤dn(Hp,Lq(−1,1)), dn(Hp,Lq(−1,1)),δn(Hp,Lq(−1,1)),<k2n12qexp(−πn2(1q−1p))Furthermore the n-widths of Hp∗ = {f analytic in the unit disk k1n12pexp(−πn2p′, ≤dn(H∗p,Lx(−1,1)), dn(H∗p,Lx(−1,1)),δn(H∗p,Lx(−1,1)),<k2exp(−πn2p′) are determined asymptotically. Let 1 < p < ∞ and p′ = p(p − 1). ThenThese results are improvements of estimates previously obtained by Burchard and Höllig and by Stenger