TRIGONOMETRIC CHAOS AND Xp INEQUALITIES, I: BALANCED FOURIER TRUNCATIONS OVER DISCRETE GROUPS
We investigate L p-estimates for balanced averages of Fourier truncations in group algebras, in terms of “differential operators” acting on them. Our results extend a fundamental inequality of Naor for the hypercube (with profound consequences in metric geometry) to discrete groups. Different inequa...
| Authors: | , , |
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| Format: | article |
| Status: | Published version |
| Publication Date: | 2024 |
| Country: | España |
| Institution: | Consejo Superior de Investigaciones Científicas (CSIC) |
| Repository: | DIGITAL.CSIC. Repositorio Institucional del CSIC |
| OAI Identifier: | oai:dnet:digitalcsic_::39cd788f976408b1f7eb8c303b953329 |
| Online Access: | http://hdl.handle.net/10261/381577 https://www.scopus.com/inward/record.uri?eid=2-s2.0-85202472590&doi=10.2140%2fapde.2024.17.2561&partnerID=40&md5=d741258728287fdc24deea1687977ca1 |
| Access Level: | Open access |
| Keyword: | Discrete groups geometry of L<sub>p</sub> spaces X<sub>p</sub> inequalities Hypercube |
| Summary: | We investigate L p-estimates for balanced averages of Fourier truncations in group algebras, in terms of “differential operators” acting on them. Our results extend a fundamental inequality of Naor for the hypercube (with profound consequences in metric geometry) to discrete groups. Different inequalities are established in terms of “directional derivatives” which are constructed via affine representations determined by the Fourier truncations. Our proofs rely on the Banach Xp nature of noncommutative L p-spaces and dimension-free estimates for noncommutative Riesz transforms. In the particular case of free groups we use an alternative approach based on free Hilbert transforms. © 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). Open Access made possible by subscribing institutions via Subscribe to Open |
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