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Sibirskii Matematicheskii Zhurnal, 2018, Volume 59, Number 6, Pages 1375–1382
DOI: https://doi.org/10.17377/smzh.2018.59.612 (Mi smj3050) 		 
The Rao–Reiter criterion for the amenability of homogeneous spaces

Ya. A. Kopylovab

a Sobolev Institute of Mathematics, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia
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DOI: https://doi.org/10.17377/smzh.2018.59.612
Abstract: We prove that a homogeneous space $G/H$, with $G$ a locally compact group and $H$ a closed subgroup of $G$, is amenable in the sense of Eymard–Greenleaf if and only if the quasiregular action $\pi_\Phi$ of $G$ on the unit sphere of the Orlicz space $L^\Phi(G/H)$ for some $N$-function $\Phi\in\Delta_2$ satisfies the Rao–Reiter condition $(P_\Phi)$.
Keywords: locally compact group, homogeneous space, amenability, $N$-function, Orlicz space, $\Delta_2$-condition.
Funding agency Grant number
Russian Academy of Sciences - Federal Agency for Scientific Organizations I.1.2, 0314-2016-0007
The author was supported by the Program of Basic Scientific Research of the Siberian Branch of the Russian Academy of Sciences (Grant No. 1.1.2, Project 0314-2016-0007).
Received: 14.11.2017
English version:
Siberian Mathematical Journal, 2018, Volume 59, Issue 6, Pages 1094–1099
DOI: https://doi.org/10.1134/S0037446618060125
Bibliographic databases:
Document Type: Article
UDC: 517.986.6
MSC: 35R30
Language: Russian
Citation: Ya. A. Kopylov, “The Rao–Reiter criterion for the amenability of homogeneous spaces”, Sibirsk. Mat. Zh., 59:6 (2018), 1375–1382; Siberian Math. J., 59:6 (2018), 1094–1099
Citation in format AMSBIB
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