Download this article
 Download this article For screen
For printing
Recent Issues

Volume 17
Issue 2, 379–756
Issue 1, 1–377

Volume 16, 10 issues

Volume 15, 8 issues

Volume 14, 8 issues

Volume 13, 8 issues

Volume 12, 8 issues

Volume 11, 8 issues

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Author Index
To Appear
 
Other MSP Journals
Directional square functions

Natalia Accomazzo, Francesco Di Plinio, Paul Hagelstein, Ioannis Parissis and Luz Roncal

Vol. 16 (2023), No. 7, 1651–1699
Abstract

Quantitative formulations of Fefferman’s counterexample for the ball multiplier are naturally linked to square function estimates for conical and directional multipliers. We develop a novel framework for these square function estimates, based on a directional embedding theorem for Carleson sequences and multiparameter time-frequency analysis techniques. As applications we prove sharp or quantified bounds for Rubio-de Francia-type square functions of conical multipliers and of multipliers adapted to rectangles pointing along N directions. A suitable combination of these estimates yields a new and currently best-known logarithmic bound for the Fourier restriction to an N-gon, improving on previous results of A. Córdoba. Our directional Carleson embedding extends to the weighted setting, yielding previously unknown weighted estimates for directional maximal functions and singular integrals.

Keywords
directional operators, directional square functions, Rubio de Francia inequalities, directional Carleson embedding theorems, polygon multiplier
Mathematical Subject Classification
Primary: 42B20
Secondary: 42B25
Milestones
Received: 28 June 2021
Revised: 9 December 2021
Accepted: 24 January 2022
Published: 21 September 2023
Authors
Natalia Accomazzo
Department of Mathematics
University of British Columbia
Vancouver, BC
Canada
Francesco Di Plinio
Dipartimento di Matematica e Applicazioni
Università di Napoli
Napoli
Italy
Paul Hagelstein
Department of Mathematics
Baylor University
Waco, TX
United States
Ioannis Parissis
Departamento de Matemáticas
Universidad del País Vasco
Bilbao
Spain
Ikerbasque
Basque Foundation for Science
Bilbao
Spain
Luz Roncal
BCAM - Basque Center for Applied Mathematics
Bilbao
Spain
Ikerbasque
Basque Foundation for Science
Bilbao
Spain

Open Access made possible by participating institutions via Subscribe to Open.