Geodesic
Weighted inequalities for quasilinear integral operators on the semi-axis and applications to Lorentz spaces
Sbornik. Mathematics, Tome 207 (2016) no. 8, pp. 1159-1186

Voir la notice de l'article provenant de la source Math-Net.Ru

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, Lorentz space.
Mots-clés : Lebesgue space 
@article{SM_2016_207_8_a6,
     author = {D. V. Prokhorov and V. D. Stepanov},
     title = {Weighted inequalities for quasilinear integral operators on the semi-axis and applications to {Lorentz} spaces},
     journal = {Sbornik. Mathematics},
     pages = {1159--1186},
     publisher = {mathdoc},
     volume = {207},
     number = {8},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2016_207_8_a6/}
}
TY  - JOUR
AU  - D. V. Prokhorov
AU  - V. D. Stepanov
TI  - Weighted inequalities for quasilinear integral operators on the semi-axis and applications to Lorentz spaces
JO  - Sbornik. Mathematics
PY  - 2016
SP  - 1159
EP  - 1186
VL  - 207
IS  - 8
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_2016_207_8_a6/
LA  - en
ID  - SM_2016_207_8_a6
ER  - 
%0 Journal Article
%A D. V. Prokhorov
%A V. D. Stepanov
%T Weighted inequalities for quasilinear integral operators on the semi-axis and applications to Lorentz spaces
%J Sbornik. Mathematics
%D 2016
%P 1159-1186
%V 207
%N 8
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_2016_207_8_a6/
%G en
%F SM_2016_207_8_a6
D. V. Prokhorov; V. D. Stepanov. Weighted inequalities for quasilinear integral operators on the semi-axis and applications to Lorentz spaces. Sbornik. Mathematics, Tome 207 (2016) no. 8, pp. 1159-1186. http://geodesic.mathdoc.fr/item/SM_2016_207_8_a6/