Russian Mathematics

, Volume 63, Issue 6, pp 1–7 | Cite as

On Invertibility of Convolution Type Operators in Morrey Spaces

  • O. G. AvsyankinEmail author


We consider integral convolution operators in the Morrey spaces. For these operators we obtain the necessary and sufficient conditions of their invertibility. Moreover, we study the Banach algebra generated by all convolution operators with summable kernels and identity operator. For this algebra we construct the symbolic calculus, in terms of which we obtain the invertibility criterion of convolution operators.

Key words

Morrey space convolution operator symbol invertibility Banach algebra 


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Author expresses deep gratitude to professor V.I. Burenkov for useful discussion of work’s results.


The work is supported by Russian Found of Fundamental Researches, grants nos. 18-01-00094-A and 18-51-06005-Az_a.


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© Allerton Press, Inc. 2019

Authors and Affiliations

  1. 1.Southern Federal UniversityRostov-on-DonRussia

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