V. D. Stepanov, G. E. Shambilova, “On the boundedness of quasilinear integral operators of iterated type with Oinarov's kernels on the cone of monotone functions”, Eurasian Math. J., 2017, Volume 8, Number 2,Pages <nobr>47

This article is cited in 4 papers

On the boundedness of quasilinear integral operators of iterated type with Oinarov's kernels on the cone of monotone functions

V. D. Stepanov^ab, G. E. Shambilova^c

^a Steklov Institute of Mathematics, 8 Gubkina St, 119991 Moscow, Russia
^b Department of Nonlinear Analysis and Optimization, RUDN University, 6 Miklukho-Maklay St, 117198 Moscow, Russia
^c Department of Mathematics, Financial University under the Government of the Russian Federation, 49 Leningradsky Prospekt, 125993 Moscow, Russia

Abstract: We solve the characterization problem of $L_v^p-L_{\rho}^r$ weighted inequalities on Lebesgue cones of monotone functions on the half-axis for quasilinear integral operators of iterated type with Oinarov's kernels.

Keywords and phrases: Hardy type inequality, weighted Lebesgue space, quasilinear integral operator, Oinarov's kernel, cone of monotone functions.

MSC: 26D15

Received: 18.11.2016

Language: English