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ON THE DOUBLING CONDITION IN THE INFINITE-DIMENSIONAL SETTING

Part of: Spaces with richer structures Abstract harmonic analysis

Published online by Cambridge University Press:  09 February 2023

DARIUSZ KOSZ Open the ORCID record for DARIUSZ KOSZ [Opens in a new window]
DARIUSZ KOSZ*
Affiliation:
Basque Center for Applied Mathematics, 48009 Bilbao, Spain and Wrocław University of Science and Technology, 50-370 Wrocław, Poland
*
e-mail: dkosz@bcamath.org
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Abstract

We present a systematic approach to the problem whether a topologically infinite-dimensional space can be made homogeneous in the Coifman–Weiss sense. The answer to the question is negative, as expected. Our leading representative of spaces with this property is $\mathbb {T}^\omega = \mathbb {T} \times \mathbb {T} \times \cdots $ with the natural product topology.

Keywords

doubling conditionquasimetric spaceinfinite-dimensional torus

MSC classification

Primary: 43A70: Analysis on specific locally compact and other abelian groups
Secondary: 54E99: None of the above, but in this section
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 108 , Issue 3 , December 2023 , pp. 480 - 491
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

The author was supported by the Basque Government (BERC 2022-2025), by the Spanish State Research Agency (SEV-2017-0718) and by the Foundation for Polish Science (START 032.2022).

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