Geodesic
Compactness of Some Operators of Convolution Type in Generalized Morrey Spaces
Matematičeskie zametki, Tome 104 (2018) no. 3, pp. 336-344.

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Sufficient conditions for the compactness in generalized Morrey spaces of the composition of a convolution operator and the operator of multiplication by an essentially bounded function are obtained. Very weak conditions on the function are also obtained under which the commutator of the operator of multiplication by such a function and a convolution operator is compact. The compactness of convolution operators in domains of cone type is investigated.
Keywords: generalized Morrey space, convolution operator, multiplication operator, commutator, compactness. 
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O. G. Avsyankin. Compactness of Some Operators of Convolution Type in Generalized Morrey Spaces. Matematičeskie zametki, Tome 104 (2018) no. 3, pp. 336-344. http://geodesic.mathdoc.fr/item/MZM_2018_104_3_a1/

[1] V. I. Burenkov, “Recent progress in studying the boundedness of classical operators of real analysis in general Morrey-type spaces. I”, Eurasian Math. J., 3:3 (2012), 11–32 | MR | Zbl

[2] V. I. Burenkov, “Recent progress in studying the boundedness of classical operators of real analysis in general Morrey-type spaces. II”, Eurasian Math. J., 4:1 (2013), 21–45 | MR | Zbl

[3] C. B. Morrey, “On the solutions of quasi-linear elliptic partial differential equations”, Trans. Amer. Math. Soc., 43:1 (1938), 126–166 | DOI | MR | Zbl

[4] V. I. Burenkov, T. V. Tararykova, “Analog neravenstva Yunga dlya svertok funktsii dlya obschikh prostranstv tipa Morri”, Funktsionalnye prostranstva, teoriya priblizhenii, smezhnye razdely matematicheskogo analiza, Tr. MIAN, 293, MAIK «Nauka/Interperiodika», M., 2016, 113–132 | DOI | MR

[5] V. I. Burenkov, T. V. Tararykova, “Young's inequality for convolutions in Morrey-type spaces”, Eurasian Math. J., 7:2 (2016), 92–99 | MR

[6] O. G. Avsyankin, “O kompaktnosti operatorov tipa svertki v prostranstvakh Morri”, Matem. zametki, 102:4 (2017), 483–489 | DOI | MR | Zbl

[7] N. A. Bokaev, V. I. Burenkov, D. T. Matin, “On the pre-compactness of a set in the generalized Morrey spaces”, Proceedings of the International Conference on Analysis and Applied Mathematics, AIP Conf. Proc., 1759, no. 1, 2016, 020108 | DOI

[8] V. I. Burenkov, Kh. V. Guliev, “Neobkhodimye i dostatochnye usloviya ogranichennosti maksimalnogo operatora v lokalnykh prostranstvakh tipa Morri”, Dokl. AN, 391:5 (2003), 591–594 | MR | Zbl

[9] V. I. Burenkov, H. V. Guliyev, “Necessary and sufficient conditions for boundedness of the maximal operator in the local Morrey-type spaces”, Studia Math., 163:2 (2004), 157–176 | DOI | MR | Zbl

[10] V. I. Burenkov, P. Jain, T. V. Tararykova, “On boundedness of the Hardy operator in Morrey-type spaces”, Eurasian Math. J., 2:1 (2011), 52–80 | MR | Zbl

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

[12] Y. Sawano, S. Sharai, “Compact commutators on Morrey spaces with non-doubling measures”, Georgian Math. J., 15:2 (2008), 353–376 | MR | Zbl

[13] Y. Chen, Y. Ding, X. Wang, “Compactness of commutators of Riesz potential on Morrey spaces”, Potential Anal., 30:4 (2009), 301–313 | DOI | MR | Zbl

[14] Y. Chen, Y. Ding, X. Wang, “Compactness of commutators for singular integrals on Morrey spaces”, Canad. J. Math., 64:2 (2012), 257–281 | DOI | MR | Zbl

[15] I. B. Simonenko, “Operatory tipa svertki v konusakh”, Matem. sb., 74 (116):2 (1967), 298–313 | MR | Zbl