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arXiv · 1905.08681

Banach-valued modulation invariant Carleson embeddings and outer-$L^p$ spaces: the Walsh case

Alex Amenta·Gennady Uraltsev
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Abstract

We prove modulation invariant embedding bounds from Bochner spaces $L^p(\mathbb{W};X)$ on the Walsh group to outer-$L^p$ spaces on the Walsh extended phase plane. The Banach space $X$ is assumed to be UMD and sufficiently close to a Hilbert space in an interpolative sense. Our embedding bounds imply $L^p$ bounds and sparse domination for the Banach-valued tritile operator, a discrete model of the Banach-valued bilinear Hilbert transform.

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Alex Amenta, Gennady Uraltsev. 2019-05-21. Banach-valued modulation invariant Carleson embeddings and outer-$L^p$ spaces: the Walsh case. https://arxiv.org/abs/1905.08681

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