New classes of function spaces and singular operators

Ghazaryan, H.; Karapetyants, A.; Margaryan, V.; Mkrtchyan, G.; Sergeev, A.

doi:10.1090/mosc/327

New classes of function spaces and singular operators
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by H. G. Ghazaryan, A. N. Karapetyants, V. N. Margaryan, G. A. Mkrtchyan and A. G. Sergeev
Translated by: Ian Marshall

Trans. Moscow Math. Soc. 2021, 273-288

DOI: https://doi.org/10.1090/mosc/327

Published electronically: March 15, 2022

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Previous version of record: Original version posted March 15, 2022
Corrected version of record: Current version corrects an error introduced by the translator. The author's name was incorrectly listed as G. G. Kazaryan. The correct name is H. G. Ghazaryan.

Abstract:

This article is dedicated to the memory of Garnik Al’bertovich Karapetyan and it contains a review of results obtained by G. A. Karapetyan and his colleagues within the joint Russian–Armenian project of RFBR. In the first section, we look at multi-anisotropic spaces which were intensively studied by Karapetyan and his students. The second section is devoted to a new class of singular Hausdorff and Hausdorff–Berezin operators. In the third section, we study the connection between real function spaces and operator algebras in a Hilbert space, established by means of a quantization procedure. UDK: 517.518.

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