Mathematics > Classical Analysis and ODEs
[Submitted on 3 Oct 2022]
Title:On the doubling condition in the infinite-dimensional setting
View PDFAbstract: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 examined 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.
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