The critical line for modulation invariant bilinear multipliers

We prove that the bilinear multipliers with symbols singular along a nondegenerate line, in the class of Muscalu, Tao and Thiele, map $L^{p_1}(\mathbb R)\times L^{p_2}(\mathbb R)$ into $L^{2/3,\infty}(\mathbb R)$ on the whole critical line \[ \frac1{p_1}+\frac1{p_2}=\frac32,\qquad 1

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-11-02
DOI
https://doi.org/10.48550/arxiv.2611.02768
Primary Topic
Advanced Harmonic Analysis Research
Type
preprint
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
preprint

The critical line for modulation invariant bilinear multipliers

Francesco Di Plinio
arXiv (Cornell University)
Advanced Harmonic Analysis Research
preprint

The critical line for modulation invariant bilinear multipliers

Francesco Di Plinio
preprint en

Abstract

We prove that the bilinear multipliers with symbols singular along a nondegenerate line, in the class of Muscalu, Tao and Thiele, map $L^{p_1}(\mathbb R)\times L^{p_2}(\mathbb R)$ into $L^{2/3,\infty}(\mathbb R)$ on the whole critical line \[ \frac1{p_1}+\frac1{p_2}=\frac32,\qquad 1

arXiv (Cornell University)
Advanced Harmonic Analysis Research
DOIOpen Access PDFOpenAlex
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.

Laika access coming soon
The critical line for modulation invariant bilinear multipliers — Francesco Di Plinio · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS