Lower bounds for the dyadic Hilbert transform
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | JAMING, Philippe | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | POZZI, Elodie | |
| hal.structure.identifier | School of Mathematics - Georgia Institute of Technology | |
| dc.contributor.author | WICK, Brett D. | |
| dc.date.accessioned | 2024-04-04T03:12:52Z | |
| dc.date.available | 2024-04-04T03:12:52Z | |
| dc.date.issued | 2018 | |
| dc.identifier.issn | 0240-2963 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/193906 | |
| dc.description.abstractEn | In this paper, we seek lower bounds of the dyadic Hilbert transform (Haar shift) of the form $\norm{\Sha f}_{L^2(K)}\geq C(I,K)\norm{f}_{L^2(I)}$where $I$ and $K$ are two dyadic intervals and $f$ supported in $I$. If $I\subset K$ such bound exist while in the other cases $K\subsetneq I$ and $K\cap I=\emptyset$ such bounds are only available under additional constraints on the derivative of $f$. In the later case, we establish a bound of the form $\norm{\Sha f}_{L^2(K)}\geq C(I,K)|\scal{f}_I|$ where $\scal{f}_I$is the mean of $f$ over $I$. This sheds new light on the similar problem for the usual Hilbert transform that we exploit. | |
| dc.description.sponsorship | Analyse Variationnelle en Tomographies photoacoustique, thermoacoustique et ultrasonore - ANR-12-BS01-0001 | |
| dc.description.sponsorship | Initiative d'excellence de l'Université de Bordeaux - ANR-10-IDEX-0003 | |
| dc.language.iso | en | |
| dc.publisher | Université Paul Sabatier _ Cellule Mathdoc | |
| dc.subject.en | Haar Shift | |
| dc.subject.en | Dyadic Hilbert transform | |
| dc.title.en | Lower bounds for the dyadic Hilbert transform | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Analyse classique [math.CA] | |
| dc.subject.hal | Mathématiques [math]/Analyse fonctionnelle [math.FA] | |
| dc.identifier.arxiv | 1605.05511 | |
| bordeaux.journal | Annales de la Faculté des Sciences de Toulouse. Mathématiques | |
| bordeaux.page | 265-284 | |
| bordeaux.volume | 27 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01317117 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01317117v1 | |
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