This article is cited in 16 papers

Weighted inequalities for quasilinear integral operators on the semi-axis and applications to Lorentz spaces

D. V. Prokhorov, V. D. Stepanov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: 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 $\Gamma$-spaces are given.
Bibliography: 41 titles.

Keywords: integral operator, weighted inequality, Lebesgue space, Lorentz space.

UDC: 517.51+517.98

MSC: Primary 26D15; Secondary 47G10

Received: 29.04.2015

DOI: 10.4213/sm8535

 English version: Sbornik: Mathematics, 2016, 207:8, 1159–1186

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