Abstract
In this paper we introduce a new function space
Funding statement: The first author was partially supported by the Science Development Foundations under the President of the Republic of Azerbaijan (Grant EIF-2013-9(15)-46/10/1) and by the grant of the Presidium of Azerbaijan National Academy of Sciences 2015.
Acknowledgements
The authors would like to express their gratitude to the anonymous reviewer for his/her comments and suggestions which improved the quality of the paper.
References
[1] O. V. Besov, V. P. Il’in and S. M. Nikolskiĭ, Integral representations of functions, and embedding theorems (in Russian), 2nd ed., Fizmatlit “Nauka”, Moscow, 1996. Search in Google Scholar
[2] V. I. Burenkov and H. V. Guliyev, Necessary and sufficient conditions for boundedness of the maximal operator in local Morrey-type spaces, Studia Math. 163 (2004), no. 2, 157–176. 10.4064/sm163-2-4Search in Google Scholar
[3] V. S. Guliyev, Generalized weighted Morrey spaces and higher order commutators of sublinear operators, Eurasian Math. J. 3 (2012), no. 3, 33–61. Search in Google Scholar
[4] V. Guliyev and Y. Sawano, Linear and sublinear operators on generalized Morrey spaces with non-doubling measures, Publ. Math. Debrecen 83 (2013), no. 3, 303–327. 10.5486/PMD.2013.5508Search in Google Scholar
[5]
V. P. Il’in,
Certain properties of functions of the spaces
[6] V. Kokilashvili, A. Meskhi and H. Rafeiro, Boundedness of commutators of singular and potential operators in generalized grand Morrey spaces and some applications, Studia Math. 217 (2013), no. 2, 159–178. 10.4064/sm217-2-4Search in Google Scholar
[7] V. Kokilashvili, A. Meskhi and H. Rafeiro, Riesz type potential operators in generalized grand Morrey spaces, Georgian Math. J. 20 (2013), no. 1, 43–64. 10.1515/gmj-2013-0009Search in Google Scholar
[8] V. Kokilashvili, A. Meskhi and H. Rafeiro, Estimates for nondivergence elliptic equations with VMO coefficients in generalized grand Morrey spaces, Complex Var. Elliptic Equ. 59 (2014), no. 8, 1169–1184. 10.1080/17476933.2013.831844Search in Google Scholar
[9] F. Q. Maksudov and A. D. Djabrailov, The Method of Integral Representations in the Theory of Spaces (in Russian), Baku, 2000. Search in Google Scholar
[10] A. L. Mazzucato, Besov–Morrey spaces: Function space theory and applications to non-linear PDE, Trans. Amer. Math. Soc. 355 (2003), no. 4, 1297–1364. 10.1090/S0002-9947-02-03214-2Search in Google Scholar
[11] C. B. Morrey, Jr., On the solutions of quasi-linear elliptic partial differential equations, Trans. Amer. Math. Soc. 43 (1938), no. 1, 126–166. 10.1090/S0002-9947-1938-1501936-8Search in Google Scholar
[12] C. B. Morrey, Jr., Second order elliptic equations in several variables and Hölder continuity, Math. Z. 72 (1959/1960), 146–164. 10.1007/BF01162944Search in Google Scholar
[13] A. M. Najafov, The imbedding theorems for the space of Besov–Morrey type with dominant mixed derivatives, Proc. Inst. Math. Mech. Natl. Acad. Sci. Azerb. 12 (2000), 97–104, 190. Search in Google Scholar
[14] A. M. Najafov, Interpolation theorem of Besov–Morrey type spaces and some its applications, Trans. Acad. Sci. Azerb. Ser. Phys. Tech. Math. Sci. 24 (2004), no. 4, 125–134. Search in Google Scholar
[15] A. Najafov, Some properties of functions from the intersection of Besov–Morrey type spaces with dominant mixed derivatives, Proc. A. Razmadze Math. Inst. 139 (2005), 71–82. Search in Google Scholar
[16] A. M. Najafov and A. T. Orujova, On properties of the generalized Besov–Morrey spaces with dominant mixed derivatives, Proc. Inst. Math. Mech. Natl. Acad. Sci. Azerb. 41 (2015), no. 1, 3–15. Search in Google Scholar
[17] Y. V. Netrusov, Some imbedding theorems for spaces of Besov–Morrey type, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 139 (1984), 139–147. 10.1007/BF01091807Search in Google Scholar
[18] J. Ross, A Morrey–Nikol’iĭ inequality, Proc. Amer. Math. Soc. 78 (1980), no. 1, 97–102. 10.1090/S0002-9939-1980-0548092-0Search in Google Scholar
[19] Y. Sawano, Identification of the image of Morrey spaces by the fractional integral operators, Proc. A. Razmadze Math. Inst. 149 (2009), 87–93. 10.1155/2009/835865Search in Google Scholar
[20] L. Tang and J. Xu, Some properties of Morrey type Besov–Triebel spaces, Math. Nachr. 278 (2005), no. 7–8, 904–917. 10.1002/mana.200310281Search in Google Scholar
© 2019 Walter de Gruyter GmbH, Berlin/Boston