Geodesic
One-sided integral operators with homogeneous kernels in grand Lebesgue spaces
Vladikavkazskij matematičeskij žurnal, Tome 19 (2017) no. 3, pp. 70-82 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Sufficient conditions and necessary conditions for the kernel and the grandiser are obtained under which one-sided integral operators with homogeneous kernels are bounded in the grand Lebesgue spaces on $\mathbb{R}$ and $\mathbb{R}^n$. Two-sided estimates for grand norms of these operators are also obtained. In addition, in the case of a radial kernel, we obtain two-sided estimates for the norms of multidimensional operators in terms of spherical means and show that this result is stronger than the inequalities for norms of operators with a nonradial kernel. 
@article{VMJ_2017_19_3_a7,
     author = {S. M. Umarkhadzhiev},
     title = {One-sided integral operators with homogeneous kernels in grand {Lebesgue} spaces},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {70--82},
     year = {2017},
     volume = {19},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2017_19_3_a7/}
}
TY  - JOUR
AU  - S. M. Umarkhadzhiev
TI  - One-sided integral operators with homogeneous kernels in grand Lebesgue spaces
JO  - Vladikavkazskij matematičeskij žurnal
PY  - 2017
SP  - 70
EP  - 82
VL  - 19
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/VMJ_2017_19_3_a7/
LA  - ru
ID  - VMJ_2017_19_3_a7
ER  - 
%0 Journal Article
%A S. M. Umarkhadzhiev
%T One-sided integral operators with homogeneous kernels in grand Lebesgue spaces
%J Vladikavkazskij matematičeskij žurnal
%D 2017
%P 70-82
%V 19
%N 3
%U http://geodesic.mathdoc.fr/item/VMJ_2017_19_3_a7/
%G ru
%F VMJ_2017_19_3_a7
S. M. Umarkhadzhiev. One-sided integral operators with homogeneous kernels in grand Lebesgue spaces. Vladikavkazskij matematičeskij žurnal, Tome 19 (2017) no. 3, pp. 70-82. http://geodesic.mathdoc.fr/item/VMJ_2017_19_3_a7/

[1] Krein S. G., Petunin Yu. I., Semenov E. M., Interpolyatsiya lineinykh operatorov, Nauka, M., 1978, 499 pp.

[2] Umarkhadzhiev S. M., “Ogranichennost lineinykh operatorov v vesovykh obobschennykh grand-prostranstvakh Lebega”, Vestn. Akad. nauk Chechenskoi resp., 19:2 (2013), 5–9

[3] Umarkhadzhiev S. M., “Obobschenie ponyatiya grand-prostranstva Lebega”, Izv. vuzov. Matematika, 2014, no. 4, 42–51

[4] Umarkhadzhiev S. M., “Ogranichennost potentsiala Rissa v vesovykh obobschennykh grand-prostranstvakh Lebega”, Vladikavk. mat. zhurn., 16:2 (2014), 62–68 | Zbl

[5] Umarkhadzhiev S. M., “Plotnost prostranstva Lizorkina v grand-prostranstvakh Lebega”, Vladikavk. mat. zhurn., 17:3 (2015), 75–83

[6] Iwaniec T., Sbordone C., “On the integrability of the Jacobian under minimal hypotheses”, Arch. Rational Mech. Anal., 119 (1992), 129–143 | DOI | MR | Zbl

[7] Karapetiants N. K., Samko S. G., Equations with Involutive Operators, Birkhäuser, Boston, 2001 | MR | Zbl

[8] Kokilashvili V., Meskhi A., Rafeiro H., Samko S., Integral Operators in Non-standard Function Spaces, v. I, Operator Theory: Advances and Appl., 248, Variable Exponent Lebesgue and Amalgam Spaces, Birkhauser, Basel, 2016, 1–586 | DOI | MR

[9] Kokilashvili V., Meskhi A., Rafeiro H., Samko S., Integral Operators in Non-Standard Function Spaces, v. II, Operator Theory: Advances and Appl., 249, Variable Exponent Holder, Morrey-Campanato and Grand Spaces, Birkhauser, Basel, 2016, 587–1009 | MR

[10] Samko S. G., Hypersingular Integrals and their Applications, Ser. Analytical Methods and Special Functions, 5, Taylor Francis, London–N. Y., 2002, 358+xvii pp. | MR | Zbl

[11] Samko S. G., Umarkhadzhiev S. M., “On Iwaniec–Sbordone spaces on sets which may have infinite measure”, Azerb. J. Math., 1:1 (2011), 67–84 | MR | Zbl

[12] Samko S. G., Umarkhadzhiev S. M., “On Iwaniec–Sbordone spaces on sets which may have infinite measure: addendum”, Azerb. J. Math., 1:2 (2011), 143–144 | MR | Zbl

[13] Samko S. G., Umarkhadzhiev S. M., “Riesz fractional integrals in grand Lebesgue spaces”, Fract. Calc. Appl. Anal., 19:3 (2016), 608–624 | DOI | MR | Zbl

[14] Samko S. G., Umarkhadzhiev S. M., “On grand Lebesgue spaces on sets of infinite measure”, Math. Nachrichten, 2016 | DOI | MR

[15] Umarkhadzhiev S. M., “The boundedness of the Riesz potential operator from generalized grand Lebesgue spaces to generalized grand Morrey spaces”, Operator Theory, Operator Algebras and Appl., Birkhäuser/Springer, Basel, 2014, 363–373 | DOI | MR | Zbl