Continuous logic and embeddings of Lebesgue spaces

Timothy H. McNicholl

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arXiv · 1805.11561

Continuous logic and embeddings of Lebesgue spaces

Timothy H. McNicholl

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Abstract

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

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BibTeX RIS

Timothy H. McNicholl. 2018-05-29. Continuous logic and embeddings of Lebesgue spaces. https://arxiv.org/abs/1805.11561

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