On some differential properties of small small Sobolev--Morrey spaces
Eurasian mathematical journal, Tome 12 (2021) no. 1, pp. 57-67.

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

In the paper small small Sobolev–Morrey spaces are constructed. Differential and differential-difference properties of functions belonging to the constructed space are studied by the integral representation method.
@article{EMJ_2021_12_1_a5,
     author = {A. M. Najafov},
     title = {On some differential properties of small small {Sobolev--Morrey} spaces},
     journal = {Eurasian mathematical journal},
     pages = {57--67},
     publisher = {mathdoc},
     volume = {12},
     number = {1},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2021_12_1_a5/}
}
TY  - JOUR
AU  - A. M. Najafov
TI  - On some differential properties of small small Sobolev--Morrey spaces
JO  - Eurasian mathematical journal
PY  - 2021
SP  - 57
EP  - 67
VL  - 12
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EMJ_2021_12_1_a5/
LA  - en
ID  - EMJ_2021_12_1_a5
ER  - 
%0 Journal Article
%A A. M. Najafov
%T On some differential properties of small small Sobolev--Morrey spaces
%J Eurasian mathematical journal
%D 2021
%P 57-67
%V 12
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EMJ_2021_12_1_a5/
%G en
%F EMJ_2021_12_1_a5
A. M. Najafov. On some differential properties of small small Sobolev--Morrey spaces. Eurasian mathematical journal, Tome 12 (2021) no. 1, pp. 57-67. http://geodesic.mathdoc.fr/item/EMJ_2021_12_1_a5/

[1] G. Anatriello, M. R. Formica, R. Giova, “Fully measurable small Lebesgue spaces”, Jour. of Mathematical Analysis and Applications, 447:1 (2017), 550–563 | DOI | MR | Zbl

[2] O. V. Besov, V. P. Il'in, S. M. Nikol'skii, Integral representation of functions and imbedding theorems, Nauka, M., 1996, 480 pp. (in Russian) | MR

[3] C. Capone, A. Fiorenza, “On small Lebesgue spaces”, Jour. of Function Spaces and Applications, 3:1 (2005), 73–89 | DOI | MR | Zbl

[4] D. Cruz-Uribe, A. Fiorenza, O. M. Guzmán, “Imbeddings of grand Morrey spaces, small Lebesgue spaces and Lebesgue spaces with variable exponent”, Matematicheskiye Zametki, 102:5-6 (2017), 736–748 (in Russian) | DOI | MR | Zbl

[5] A. Eroglu, J. V. Azizov, V. S. Guliyev, “Fractional maximal operator and its commutators in generalized Morrey spaces on Heisenberg group”, Proc. of Inst. Math. and Mechanics NAS Azerb., 44:2 (2018), 304–317 | MR | Zbl

[6] A. Fiorenza, C. E. Karadzhov, “Grand and small Lebesgue spaces and their anologues”, J. Anal. Appl., 23:4 (2004), 657–681 | MR | Zbl

[7] A. Fiorenza, M. R. Formica, A. Gogatishvili, “On grand and small Lebesgue spaces and some applications to PDE's”, Differential Equations and Applications, 10:1 (2018), 21–46 | DOI | MR | Zbl

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

[9] V. M. Kokilashvili, A. Meskhi, “Trace inequalities for fractional integrals in grand Lebesgue spaces”, Studia Math., 210:2 (2012), 159–176 | DOI | MR | Zbl

[10] Y. Liang, D. Yang, W. Yuan, S. Sawano, T. Ullrich, “A new framework for generalized Besov-type and Triebel-Lizorkin-type spaces”, Dissertationes Mathematicae, 489 (2013), 1–114 | DOI | MR

[11] A. Meskhi, Y. Sawano, Density, duality and preduality in grand variable exponent Lebesgue and Morrey spaces, 06 0ct. 2017, arXiv: 1710.02383v1 [math.FA] | MR

[12] Y. Mizuta, T. Ohno, “Trudingers exponential integrability for Reisz potentials of function in generalized grand Morrey spaces”, J. Math. Anal. Appl., 420:1 (2014), 268–278 | DOI | MR | Zbl

[13] A. M. Najafov, “On some properties of functions from Sobolev-Morrey type spaces”, Sibirskii Matem. Zhurnal, 46:3 (2005), 634–648 (in Russian) | MR

[14] A. M. Najafov, A. T. Orujova, “On the solution of a class of partial differential equations”, Electron. J. Qual. Theory Differ. Equ., 2017, no. 44, 1–9 | DOI | MR

[15] A. M. Najafov, N. R. Rustamova, “On properties of functions from Sobolev-Morrey type spaces with dominant mixed derivatives”, Trans. of National Academy of Sciences of Azerbaijan, Issue Math., 37:4 (2017), 132–141 | MR | Zbl

[16] A. M. Najafov, N. R. Rustamova, “Some differential properties of anisotropic grand Sobolev-Morrey spaces”, Trans. of A. Razmadze Mathematical Institute, 172 (2018), 82–89 | DOI | MR | Zbl

[17] H. Rafeiro, “A note on boundedness of operators in grand grand Morrey spaces”, Advances in Harmonic Analysis and Operator Theory, 2013, 349–356 | DOI | MR | Zbl

[18] C. Sbordone, “Grand Sobolev spaces and their applications to variational problems”, Le Mathematiche, 1:11 (1996), 335–347 | MR

[19] S. M. Umarkhadziev, “The boundedness of the Riesz potential operator from generalized grand Lebesgue spaces to generalized grand Morrey spaces”, Operator theory: Advances and Applications, 242 (2014), 363–373 | DOI | MR