Geodesic
On the boundedness of some classes of integral operators in weighted Lebesgue spaces
Eurasian mathematical journal, Tome 3 (2012) no. 1, pp. 5-17.

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

Some new Hardy-type inequalities for Hardy-Volterra integral operators are proved and discussed. The case $1$ is considered and the involved kernels satisfy conditions, which are less restrictive than the usual Oinarov condition. 
@article{EMJ_2012_3_1_a0,
     author = {L. S. Arendarenko and R. Oinarov and L.-E. Persson},
     title = {On the boundedness of some classes of integral operators in weighted {Lebesgue} spaces},
     journal = {Eurasian mathematical journal},
     pages = {5--17},
     publisher = {mathdoc},
     volume = {3},
     number = {1},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2012_3_1_a0/}
}
TY  - JOUR
AU  - L. S. Arendarenko
AU  - R. Oinarov
AU  - L.-E. Persson
TI  - On the boundedness of some classes of integral operators in weighted Lebesgue spaces
JO  - Eurasian mathematical journal
PY  - 2012
SP  - 5
EP  - 17
VL  - 3
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EMJ_2012_3_1_a0/
LA  - en
ID  - EMJ_2012_3_1_a0
ER  - 
%0 Journal Article
%A L. S. Arendarenko
%A R. Oinarov
%A L.-E. Persson
%T On the boundedness of some classes of integral operators in weighted Lebesgue spaces
%J Eurasian mathematical journal
%D 2012
%P 5-17
%V 3
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EMJ_2012_3_1_a0/
%G en
%F EMJ_2012_3_1_a0
L. S. Arendarenko; R. Oinarov; L.-E. Persson. On the boundedness of some classes of integral operators in weighted Lebesgue spaces. Eurasian mathematical journal, Tome 3 (2012) no. 1, pp. 5-17. http://geodesic.mathdoc.fr/item/EMJ_2012_3_1_a0/

[1] T. Ando, “On compactness of integral operators”, Nederl. Akad. Wetensch. Proc. Ser. A 65 = Indag. Math., 24 (1962), 235–239 | MR

[2] V. Kokilashvili, A. Meskhi, L.-E. Persson, Weighted norm inequalities for integral transforms with product kernels, Mathematics Research Development Series, New York, 2010 | MR

[3] A. Kufner, L. Maligranda, L.-E. Persson, The Hardy inequality. About its history and some related results, Vydavatelsky Servis, Pilsen, 2007 | MR | Zbl

[4] A. Kufner, L.-E. Persson, Weighted inequalities of Hardy type, World Scientific, New Jersey, 2003 | MR | Zbl

[5] Soviet Math. Dokl., 44:1 (1992), 291–293 | MR

[6] Proc. Steklov Inst. Math., 204:3 (1994), 205–214 | MR | Zbl

[7] Siberian Math J., 48:5 (2007), 884–896 | DOI | MR | Zbl

[8] B. Opic, A. Kufner, Hardy-type inequalities, Pitman Research Notes in Mathematics, 219, Longman Science and Technology, Harlow, 1990 | MR | Zbl