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 Mat. Zametki, 2018, Volume 104, Issue 3, Pages 336–344 (Mi mz12108)

Compactness of Some Operators of Convolution Type in Generalized Morrey Spaces

O. G. Avsyankin

Southern Federal University, Rostov-on-Don

Abstract: 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.

 Funding Agency Grant Number Russian Foundation for Basic Research 18-01-00094-A18-51-06005-Àç_à This work was financially supported by the Russian Foundation for Basic Research under grants no. 18-01-00094-A and no. 18-51-06005-Az_a.

DOI: https://doi.org/10.4213/mzm12108

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English version:
Mathematical Notes, 2018, 104:3, 331–338

Bibliographic databases:

UDC: 517.9

Citation: O. G. Avsyankin, “Compactness of Some Operators of Convolution Type in Generalized Morrey Spaces”, Mat. Zametki, 104:3 (2018), 336–344; Math. Notes, 104:3 (2018), 331–338

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/mz12108
• https://doi.org/10.4213/mzm12108
• http://mi.mathnet.ru/eng/mz/v104/i3/p336

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This publication is cited in the following articles:
1. O. G. Avsyankin, “Ob integralnykh operatorakh s periodicheskimi yadrami v prostranstvakh summiruemykh funktsii”, Izv. vuzov. Matem., 2020, no. 2, 3–9
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