JAMING, Philippe; POZZI, Elodie; WICK, Brett D.

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Licencia de uso del documento

JAMING, Philippe
Institut de Mathématiques de Bordeaux [IMB]

POZZI, Elodie
Institut de Mathématiques de Bordeaux [IMB]

WICK, Brett D.
School of Mathematics - Georgia Institute of Technology

Idioma

Article de revue

Este ítem está publicado en

Annales de la Faculté des Sciences de Toulouse. Mathématiques. 2018, vol. 27, p. 265-284

Université Paul Sabatier _ Cellule Mathdoc

Resumen en inglés

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.< Leer menos

Palabras clave en inglés

Haar Shift

Dyadic Hilbert transform

URI

https://oskar-bordeaux.fr/handle/20.500.12278/193906

Proyecto ANR

Analyse Variationnelle en Tomographies photoacoustique, thermoacoustique et ultrasonore - ANR-12-BS01-0001
Initiative d'excellence de l'Université de Bordeaux - ANR-10-IDEX-0003

Orígen

Importado de Hal

Centros de investigación

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251