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Weighted inequalities for quasilinear integral operators on the semi-axis and applications to Lorentz spaces. (English. Russian original) Zbl 1365.26022

Sb. Math. 207, No. 8, 1159-1186 (2016); translation from Mat. Sb. 207, No. 7, 135-162 (2016).
The authors derived and proved the characterization of inequalities in weighted Lebesgue spaces with positive quasilinear integral operators of iterative type on the half-axis. Furthermore, the solution of the problem of boundedness of the Hardy-Littlewood maximal operator in weighted Lorentz \(\Gamma\)-spaces for all \(p\) and \(q\), \(0< p,q< \infty\) are also given.

MSC:

26D15 Inequalities for sums, series and integrals
47G10 Integral operators
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References:

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