Continuous logic and embeddings of Lebesgue spaces

Archive for Mathematical Logic 60 (1):105-119 (2020)
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Abstract

We use the compactness theorem of continuous logic to give a new proof that Lr([0,1];R)L^r([0,1]; {\mathbb {R}}) isometrically embeds into Lp([0,1];R)L^p([0,1]; {\mathbb {R}}) whenever 1≤p≤r≤21 \le p \le r \le 2. We will also give a proof for the complex case. This will involve a new characterization of complex LpL^p spaces based on Banach lattices.

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2021

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10.1007/s00153-020-00734-7

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