New equivalence theorems for weighted inequalities involving the composition of monotone quasilinear operators with the Hardy and Copson operators and their applications

Abstract: In this paper, new equivalence theorems for the boundedness of the composition of a quasilinear operator $T$ with the Hardy and Copson operators in weighted Lebesgue spaces are proved. The usefulness of the obtained results is illustrated in the case of weighted Hardy-type and weighted iterated Hardy-type inequalities.