Research Article
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Year 2023, Volume: 72 Issue: 2, 429 - 437, 23.06.2023
https://doi.org/10.31801/cfsuasmas.1171026

Abstract

References

  • Besov, O. V., Ilyin, V. P., Nikolskii, S. M., Integralnye Predstavleniya Funktsi i Teoremy Vlozheniya (Russian) (Integral Representations of Functions and Embedding Theorems), Fizmatlit ”Nauka”, Moscow, 1996.
  • Fiorenza, A., Formica, M., Gogatishvili, A., On grand and small Lebesgue equations and applications, Differ. Equ. Appl., 10(1) (2018), 21-46. dx.doi.org/10.7153/dea-2018-10-03
  • He, S., Tao, Sh., Boundedness of some operators on grand generalized Morrey spaces over nonhomogeneous spaces, AIMS Mathematics, 7(1) (2022), 1000-1014. doi:10.39341 math.2022060
  • Iwaniec, T., Sbordone, C., On the integrability of the Jacobian under minimal hypoteses, Arch. Rational Mech. Anal., 119(2) (1992), 129-143. https://doi.org/10.1007/BF00375119
  • Kokilashvili, V. M., Meskhi, A., Rafeiro, H., Riesz type potential operators in generalized grand Morrey spaces, Georgian Math. J., 20(1) (2013), 43-64. https://doi.org/10.1515/gmj-2013-0009
  • Liu, Y., Yuan, W., Interpolation and duality of generalized grand Morrey spaces on quasi-metric measure spaces, Czechoslovak Math. J., 67(3) (2017), 715-732. DOI:10.21136/CMJ.2017.0081-16
  • Meskhi, A., Maximal functions potentials and singular integrals in grand Morrey spaces, Comp. Var. Ellip. Equations, 56(10-11) (2011), 1003-1019. https://doi.org/10.1080/17476933.2010.534793
  • Mizuta, Y., Ohno, T., Trudingers exponential integrability for Riesz potentials of function in generalized grand Morrey spaces, J. Math. Anal. Appl., 420(1) (2014). https://doi.org/10.1016/j.jmaa.2014.05.082
  • Najafov, A. M., Alekberli, S. T., On properties of functions from grand Sobolev-Morrey spaces, J. Baku Engineering Univ., 2(1) (2018), 27-36.
  • Najafov, A. M., Rustamova, N. R., Some differential properties of anisotropic grand Sobolev Morrey spaces, Trans. A. Razmadze Math. Inst., 172(1) (2018), 82-89. https://doi.org/10.1016/j.trmi.2017.10.001
  • Najafov, A. M., Gasimova, A. M., On embedding theorems in grand grand Nikolski-Morrey spaces, Eur. J. Pure Appl. Math., 12(4) (2019), 1602-1611. https://doi.org/10.29020/nybg.ejpam.v12i4.3567
  • Najafov, A. M., On some properties differential properties of small small Sobolev-Morrey spaces, Eurasian Math. J., 12(1) (2021), 57-67. https://doi.org/10.32523/2077-9879-2021-12-1-57-67
  • Rafeiro, H., A note on boundedness of operators in grand grand Morrey spaces, Operator Theory: Advances and Applications, 229 (2013) 349–356. DOI:10.1007/978-3-0348-0516-2 19
  • Umarkhadzhiev, S., The boundedness of the Riesz potential operator from generalized grand Lebesgue spaces to generalized grand Morrey spaces, Operator Theory, Operator Algebras and Applications, 363-373, Oper. Theory Adv. Appl., 242, Birkh¨auser, Springer, Basel, 2014. DOI:10.1007/978-3-0348-0816-3 22

On some differential properties of functions in generalized grand Sobolev-Morrey spaces

Year 2023, Volume: 72 Issue: 2, 429 - 437, 23.06.2023
https://doi.org/10.31801/cfsuasmas.1171026

Abstract

In this paper we introduce a generalized grand Sobolev-Morrey spaces. Some differential and differential-difference properties of functions from this spaces are proved by means of the integral representation.

References

  • Besov, O. V., Ilyin, V. P., Nikolskii, S. M., Integralnye Predstavleniya Funktsi i Teoremy Vlozheniya (Russian) (Integral Representations of Functions and Embedding Theorems), Fizmatlit ”Nauka”, Moscow, 1996.
  • Fiorenza, A., Formica, M., Gogatishvili, A., On grand and small Lebesgue equations and applications, Differ. Equ. Appl., 10(1) (2018), 21-46. dx.doi.org/10.7153/dea-2018-10-03
  • He, S., Tao, Sh., Boundedness of some operators on grand generalized Morrey spaces over nonhomogeneous spaces, AIMS Mathematics, 7(1) (2022), 1000-1014. doi:10.39341 math.2022060
  • Iwaniec, T., Sbordone, C., On the integrability of the Jacobian under minimal hypoteses, Arch. Rational Mech. Anal., 119(2) (1992), 129-143. https://doi.org/10.1007/BF00375119
  • Kokilashvili, V. M., Meskhi, A., Rafeiro, H., Riesz type potential operators in generalized grand Morrey spaces, Georgian Math. J., 20(1) (2013), 43-64. https://doi.org/10.1515/gmj-2013-0009
  • Liu, Y., Yuan, W., Interpolation and duality of generalized grand Morrey spaces on quasi-metric measure spaces, Czechoslovak Math. J., 67(3) (2017), 715-732. DOI:10.21136/CMJ.2017.0081-16
  • Meskhi, A., Maximal functions potentials and singular integrals in grand Morrey spaces, Comp. Var. Ellip. Equations, 56(10-11) (2011), 1003-1019. https://doi.org/10.1080/17476933.2010.534793
  • Mizuta, Y., Ohno, T., Trudingers exponential integrability for Riesz potentials of function in generalized grand Morrey spaces, J. Math. Anal. Appl., 420(1) (2014). https://doi.org/10.1016/j.jmaa.2014.05.082
  • Najafov, A. M., Alekberli, S. T., On properties of functions from grand Sobolev-Morrey spaces, J. Baku Engineering Univ., 2(1) (2018), 27-36.
  • Najafov, A. M., Rustamova, N. R., Some differential properties of anisotropic grand Sobolev Morrey spaces, Trans. A. Razmadze Math. Inst., 172(1) (2018), 82-89. https://doi.org/10.1016/j.trmi.2017.10.001
  • Najafov, A. M., Gasimova, A. M., On embedding theorems in grand grand Nikolski-Morrey spaces, Eur. J. Pure Appl. Math., 12(4) (2019), 1602-1611. https://doi.org/10.29020/nybg.ejpam.v12i4.3567
  • Najafov, A. M., On some properties differential properties of small small Sobolev-Morrey spaces, Eurasian Math. J., 12(1) (2021), 57-67. https://doi.org/10.32523/2077-9879-2021-12-1-57-67
  • Rafeiro, H., A note on boundedness of operators in grand grand Morrey spaces, Operator Theory: Advances and Applications, 229 (2013) 349–356. DOI:10.1007/978-3-0348-0516-2 19
  • Umarkhadzhiev, S., The boundedness of the Riesz potential operator from generalized grand Lebesgue spaces to generalized grand Morrey spaces, Operator Theory, Operator Algebras and Applications, 363-373, Oper. Theory Adv. Appl., 242, Birkh¨auser, Springer, Basel, 2014. DOI:10.1007/978-3-0348-0816-3 22
There are 14 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Alik Najafov 0000-0002-4289-9056

Ahmet Eroğlu 0000-0002-2642-3154

Firide Mustafayeva 0000-0002-0738-4911

Publication Date June 23, 2023
Submission Date September 6, 2022
Acceptance Date December 9, 2022
Published in Issue Year 2023 Volume: 72 Issue: 2

Cite

APA Najafov, A., Eroğlu, A., & Mustafayeva, F. (2023). On some differential properties of functions in generalized grand Sobolev-Morrey spaces. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 72(2), 429-437. https://doi.org/10.31801/cfsuasmas.1171026
AMA Najafov A, Eroğlu A, Mustafayeva F. On some differential properties of functions in generalized grand Sobolev-Morrey spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. June 2023;72(2):429-437. doi:10.31801/cfsuasmas.1171026
Chicago Najafov, Alik, Ahmet Eroğlu, and Firide Mustafayeva. “On Some Differential Properties of Functions in Generalized Grand Sobolev-Morrey Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72, no. 2 (June 2023): 429-37. https://doi.org/10.31801/cfsuasmas.1171026.
EndNote Najafov A, Eroğlu A, Mustafayeva F (June 1, 2023) On some differential properties of functions in generalized grand Sobolev-Morrey spaces. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72 2 429–437.
IEEE A. Najafov, A. Eroğlu, and F. Mustafayeva, “On some differential properties of functions in generalized grand Sobolev-Morrey spaces”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 72, no. 2, pp. 429–437, 2023, doi: 10.31801/cfsuasmas.1171026.
ISNAD Najafov, Alik et al. “On Some Differential Properties of Functions in Generalized Grand Sobolev-Morrey Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72/2 (June 2023), 429-437. https://doi.org/10.31801/cfsuasmas.1171026.
JAMA Najafov A, Eroğlu A, Mustafayeva F. On some differential properties of functions in generalized grand Sobolev-Morrey spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2023;72:429–437.
MLA Najafov, Alik et al. “On Some Differential Properties of Functions in Generalized Grand Sobolev-Morrey Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 72, no. 2, 2023, pp. 429-37, doi:10.31801/cfsuasmas.1171026.
Vancouver Najafov A, Eroğlu A, Mustafayeva F. On some differential properties of functions in generalized grand Sobolev-Morrey spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2023;72(2):429-37.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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