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

2019/05/21 by Alex Amenta, Amenta, Alex, Gennady Uraltsev +1
Mathematics · #47A56 #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Primary: 42B20 #Secondary: 42B25

paper · pdf · doi:10.48550/arxiv.1905.08681

openalex publication_date 2019/05/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove modulation invariant embedding bounds from Bochner spaces\nL^p( mathbbW;X) on the Walsh group to outer-L^p spaces on the Walsh\nextended phase plane. The Banach space X is assumed to be UMD and\nsufficiently close to a Hilbert space in an interpolative sense. Our embedding\nbounds imply L^p bounds and sparse domination for the Banach-valued tritile\noperator, a discrete model of the Banach-valued bilinear Hilbert transform.\n

Related

• The bilinear Hilbert transform in UMD spaces
• A modulation invariant Carleson embedding theorem outside local L²
• Banach-valued multilinear singular integrals with modulation invariance
• Variational Carleson embeddings into the upper 3-space
• Modulation invariant operators