The fine structure of the \(n\)-widths of \(H^ p\)-spaces in \(L_ q(-1,1)\) (Q1908043)

Let \(\Delta \subset \mathbb{C}\) be the open unit disk. The precise asymptotic behaviour of the Kolmogorov, Gel'fand, and linear \(n\)-widths of the unit ball of the Hardy space \(H^p (\Delta)\) in \(L_p (-1, 1)\) for \(1\leq q< p\leq \infty\) are determined. This result extends estimates previously obtained by \textit{H. G. Burchard} and \textit{K. Höllig} [SIAM J. Math. Anal. 16, 405-421 (1985; Zbl 0554.41030)] and by the author [J. Complexity 8, No. 3, 324-335 (1992; Zbl 0803.46056)].