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A Marcinkiewicz
multiplier theory for Schur multipliers
Chian Yeong Chuah, Zhen-Chuan Liu and Tao Mei |
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Vol. 18 (2025), No. 6, 1511–1530
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Abstract |
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We prove a Marcinkiewicz-type multiplier theory for the boundedness of Schur multipliers on the Schatten -classes. This generalizes a previous result of J. Bourgain for Toeplitz-type Schur multipliers and complements a recent result by J. Conde-Alonso et al. (Ann. of Math. 198:3 (2023), 1229–1260). As a corollary, we obtain a new unconditional decomposition for the Schatten -classes, . We extend our main result to the and cases, and include an operator-valued version of it using Pisier’s noncommutative -norm. |
Keywords
Schur multipliers, Schatten $p$-classes, Littlewood–Paley
theory, Marcinkiewicz multiplier theory, noncommutative
$L^p$ spaces
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Mathematical Subject Classification
Primary: 46B28, 46L52
Secondary: 42A45
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Milestones
Received: 9 November 2023
Revised: 24 April 2024
Accepted: 24 May 2024
Published: 29 May 2025
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Authors |
| Chian Yeong Chuah | |
| Department of Mathematics The Ohio State University Columbus, OH United States |
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| Zhen-Chuan Liu | |
| Departamento de Matemáticas Universidad Autónoma de Madrid Madrid Spain |
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| Tao Mei | |
| Department of Mathematics Baylor University Waco, TX United States |
Department of Mathematics Texas A&M University College Station, TX United States |
| © 2025 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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