Author:
Amenta Alex,Uraltsev Gennady
Abstract
AbstractWe prove modulation invariant embedding bounds from Bochner spaces $$L^p(\mathbb {W};X)$$
L
p
(
W
;
X
)
on the Walsh group to outer-$$L^p$$
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 $$L^p$$
L
p
bounds and sparse domination for the Banach-valued tritile operator, a discrete model of the Banach-valued bilinear Hilbert transform.
Funder
Rheinische Friedrich-Wilhelms-Universität Bonn
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,General Mathematics,Analysis
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