Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2026 / Volume: 72 Issue: 2

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

Alik Najafov(AZERBAIJAN ARCHITECTURE AND CONSTRUCTION UNIVERSITY)0000-0002-4289-9056
Ahmet Eroğlu(NIGDE OMER HALISDEMIR UNIVERSITY)0000-0002-2642-3154
Firide Mustafayeva(AZERBAIJAN STATE PEDOGOGICAL UNIVERSITY)0000-0002-0738-4911
Pages
—
Publication Date
2023-06-23
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Some differential and differential-difference properties of functions from this spaces are proved by means of the integral representation.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper we introduce a generalized grand Sobolev-Morrey spaces.
📊
Key Findings & Data:In this paper we introduce a generalized grand Sobolev-Morrey spaces.
💡
Conclusion & Impact:Some differential and differential-difference properties of functions from this spaces are proved by means of the integral representation.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Generalized grand Sobolev-Morrey spaces · integral representation · flexible-horn condition

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.

🔖

Cite This Article

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, Volume: 72 Issue: 2. https://doi.org/10.31801/cfsuasmas.1171026

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (14)

  1. 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.
  2. 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
  3. 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
  4. 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
  5. 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
  6. 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
  7. 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
  8. 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
  9. Najafov, A. M., Alekberli, S. T., On properties of functions from grand Sobolev-Morrey spaces, J. Baku Engineering Univ., 2(1) (2018), 27-36.
  10. 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
  11. 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
  12. 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
  13. 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
  14. 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