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Directional square
functions
Natalia Accomazzo, Francesco Di Plinio, Paul Hagelstein, Ioannis Parissis and Luz Roncal |
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Vol. 16 (2023), No. 7, 1651–1699
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Abstract |
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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 directions. A suitable combination of these estimates yields a new and currently best-known logarithmic bound for the Fourier restriction to an -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
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Mathematical Subject Classification
Primary: 42B20
Secondary: 42B25
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Milestones
Received: 28 June 2021
Revised: 9 December 2021
Accepted: 24 January 2022
Published: 21 September 2023
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Authors |
| Natalia Accomazzo | |
| Department of Mathematics University of British Columbia Vancouver, BC Canada |
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| Francesco Di Plinio | |
| Dipartimento di Matematica e
Applicazioni Università di Napoli Napoli Italy |
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| Paul Hagelstein | |
| Department of Mathematics Baylor University Waco, TX United States |
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| 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 |
| © 2023 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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