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[en] A precise characterization of inequalities in weighted Lebesgue spaces with positive quasilinear integral operators of iterative type on the half-axis is given. All cases of positive integration parameters are treated, including the case of supremum. Applications to the solution of the well-known problem of the boundedness of the Hardy-Littlewood maximal operator in weighted Lorentz -spaces are given. Bibliography: 41 titles.
Journal
Sbornik. Mathematics; ISSN 1064-5616; 
; v. 207(8); p. 1159-1186
; v. 207(8); p. 1159-1186