Geodesic
On Two-Dimensional Bilinear Inequalities with Rectangular Hardy Operators in Weighted Lebesgue Spaces
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function Spaces, Approximation Theory, and Related Problems of Analysis, Tome 312 (2021), pp. 251-258.

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

We characterize a two-dimensional bilinear inequality with rectangular Hardy operators in weighted norms of Lebesgue spaces. 
@article{TM_2021_312_a14,
     author = {V. D. Stepanov and G. E. Shambilova},
     title = {On {Two-Dimensional} {Bilinear} {Inequalities} with {Rectangular} {Hardy} {Operators} in {Weighted} {Lebesgue} {Spaces}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {251--258},
     publisher = {mathdoc},
     volume = {312},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2021_312_a14/}
}
TY  - JOUR
AU  - V. D. Stepanov
AU  - G. E. Shambilova
TI  - On Two-Dimensional Bilinear Inequalities with Rectangular Hardy Operators in Weighted Lebesgue Spaces
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2021
SP  - 251
EP  - 258
VL  - 312
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2021_312_a14/
LA  - ru
ID  - TM_2021_312_a14
ER  - 
%0 Journal Article
%A V. D. Stepanov
%A G. E. Shambilova
%T On Two-Dimensional Bilinear Inequalities with Rectangular Hardy Operators in Weighted Lebesgue Spaces
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2021
%P 251-258
%V 312
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2021_312_a14/
%G ru
%F TM_2021_312_a14
V. D. Stepanov; G. E. Shambilova. On Two-Dimensional Bilinear Inequalities with Rectangular Hardy Operators in Weighted Lebesgue Spaces. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function Spaces, Approximation Theory, and Related Problems of Analysis, Tome 312 (2021), pp. 251-258. http://geodesic.mathdoc.fr/item/TM_2021_312_a14/

[1] Aguilar Cañestro M.I., Ortega Salvador P., Ramírez Torreblanca C., “Weighted bilinear Hardy inequalities”, J. Math. Anal. Appl., 387:1 (2012), 320–334 | DOI | MR | Zbl

[2] Bilgiçli N., Mustafayev R.Ch., Ünver T., “Multidimensional bilinear Hardy inequalities”, Azerb. J. Math., 10:1 (2020), 127–161 | MR | Zbl

[3] Cwikel M., Kerman R., “Positive multilinear operators acting on weighted $L^p$ spaces”, J. Funct. Anal., 106:1 (1992), 130–144 | DOI | MR | Zbl

[4] Grafakos L., Torres R.H., “A multilinear Schur test and multiplier operators”, J. Funct. Anal., 187:1 (2001), 1–24 | DOI | MR | Zbl

[5] Jain P., Kanjilal S., Persson L.-E., “Hardy-type inequalities over balls in $\mathbb R^N$ for some bilinear and iterated operators”, J. Inequal. Spec. Funct., 10:2 (2019), 35–48 | MR

[6] P. Jain, S. Kanjilal, V. D. Stepanov, and E. P. Ushakova, “On bilinear Hardy–Steklov operators”, Dokl. Math., 98:3 (2018), 634–637 | DOI | MR | Zbl

[7] Jain P., Kanjilal S., Stepanov V.D., Ushakova E.P., “Bilinear Hardy–Steklov operators”, Math. Notes, 104:6 (2018), 823–832 | DOI | MR | Zbl

[8] Křepela M., “Iterating bilinear Hardy inequalities”, Proc. Edinb. Math. Soc. Ser. 2, 60:4 (2017), 955–971 | DOI | MR

[9] Křepela M., “Bilinear weighted Hardy inequality for nonincreasing functions”, Publ. Mat. Barc., 61:1 (2017), 3–50 | DOI | MR

[10] Kufner A., Persson L.-E., Samko N., Weighted inequalities of Hardy type, 2nd ed., World Scientific, Hackensack, NJ, 2017 | MR | Zbl

[11] Persson L.-E., Ushakova E.P., “Some multi-dimensional Hardy type integral inequalities”, J. Math. Inequal., 1:3 (2007), 301–319 | DOI | MR | Zbl

[12] D. V. Prokhorov, “On a class of weighted inequalities containing quasilinear operators”, Proc. Steklov Inst. Math., 293 (2016), 272–287 | DOI | MR | MR | Zbl

[13] D. V. Prokhorov, V. D. Stepanov, and E. P. Ushakova, “Hardy–Steklov integral operators. I, II”, Proc. Steklov Inst. Math., 300:Suppl. 2 (2018), S1–S112 ; 302:Suppl. 1 (2018), S1–S61 | MR | MR | Zbl | Zbl

[14] Sawyer E., “Weighted inequalities for the two-dimensional Hardy operator”, Stud. math., 82 (1985), 1–16 | DOI | MR | Zbl

[15] V. D. Stepanov and G. E. Shambilova, “Reduction of weighted bilinear inequalities with integration operators on the cone of nondecreasing functions”, Sib. Math. J., 59:3 (2018), 505–522 | DOI | MR | Zbl

[16] Stepanov V.D., Shambilova G.E., “On iterated and bilinear integral Hardy-type operators”, Math. Inequal. Appl., 22:4 (2019), 1505–1533 | MR | Zbl

[17] V. D. Stepanov and G. E. Shambilova, “Multidimensional bilinear Hardy inequalities”, Dokl. Math., 100:1 (2019), 374–376 | DOI | MR | Zbl

[18] V. D. Stepanov and G. E. Shambilova, “Multidimensional bilinear Hardy inequalities”, Sib. Math. J., 61:4 (2020), 725–742 | DOI | MR | Zbl

[19] Stepanov V.D., Ushakova E.P., “Bilinear Hardy-type inequalities in weighted Lebesgue spaces”, Nonlinear Stud., 26:4 (2018), 939–953 | MR

[20] Wedestig A., “Weighted inequalities for the Sawyer two-dimensional Hardy operator and its limiting geometric mean operator”, J. Inequal. Appl., 2005:4 (2005), 387–394 | DOI | MR | Zbl