Banach-Valued Modulation Invariant Carleson Embeddings and Outer-$$L^p$$ Spaces: The Walsh Case

@article{Amenta2019BanachValuedMI,
  title={Banach-Valued Modulation Invariant Carleson Embeddings and Outer-\$\$L^p\$\$ Spaces: The Walsh Case},
  author={Alex Amenta and Gennady N. Uraltsev},
  journal={arXiv: Classical Analysis and ODEs},
  year={2019}
}
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. 
5 Citations
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