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We prove sharp end forms of Holmstedt's reiteration theorem which are closely connected with a general form of Gehring's Lemma. Reverse type conditions for the Hardy-Littlewood-Polya order are considered and the maximal elements are shown to satisfy generalized Gehring conditions. The methods we use are elementary and based on variants of reverse Hardy inequalities for monotone functions.doi:10.4064/sm-142-1-7-24 fatcat:qhq2inolbfa5jpcqzwo2u64yda