Chebyshev polynomial iterations and approximate solutions of linear operator equations

Using several types of reversed Hölder inequalities (which hold for functions defined on (0,infty) satisfying one or two conditions of quasi-monotonicity) the authors employ results from their previous paper [Acta Sci. Math. (Szeged) {bf 59} (1994), no.~1-2, 221--239; [msn] MR1285442 (95f:26021) [/msn]] to obtain reversed Hardy inequalities for other ranges of parameters. More precisely, they prove that under suitable assumptions on the parameters A, B, p, q the inequalities |xsp A(Hsb if)(x)|sb{Lsp q}le C|xsp B f(x)|sb{Lsp p}quad(i=1,2) (where 0