Lower bounds for the dyadic Hilbert transform
| Autor: | Brett D. Wick, Elodie Pozzi, Philippe Jaming |
|---|---|
| Přispěvatelé: | Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), School of Mathematics - Georgia Institute of Technology, Georgia Institute of Technology [Atlanta], National Science Foundation DMS grants DMS \# 1603246 and \# 1560955, AMADEUS project 35598VB - ChargeDisq, CMCU/UTIQUE project 32701UB Popart, ANR-12-BS01-0001,AVENTURES,Analyse Variationnelle en Tomographies photoacoustique, thermoacoustique et ultrasonore(2012), ANR-10-IDEX-0003,IDEX BORDEAUX,Initiative d'excellence de l'Université de Bordeaux(2010) |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
010102 general mathematics
Haar 010103 numerical & computational mathematics General Medicine [MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA] [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA] 01 natural sciences Dyadic Hilbert transform Functional Analysis (math.FA) Combinatorics Mathematics - Functional Analysis symbols.namesake Haar Shift Mathematics - Classical Analysis and ODEs Norm (mathematics) symbols Classical Analysis and ODEs (math.CA) FOS: Mathematics Hilbert transform 0101 mathematics 42B20 Mathematics |
| Zdroj: | Annales de la Faculté des Sciences de Toulouse. Mathématiques. Annales de la Faculté des Sciences de Toulouse. Mathématiques., Université Paul Sabatier _ Cellule Mathdoc 2018, 27, pp.265-284 |
| ISSN: | 0240-2963 2258-7519 |
| Popis: | In this paper, we seek lower bounds of the dyadic Hilbert transform (Haar shift) of the form $\left\Vert S f\right\Vert_{L^2(K)}\geq C(I,K)\left\Vert f\right\Vert_{L^2(I)}$ 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 $\left\Vert S f\right\Vert_{L^2(K)}\geq C(I,K)|\left\langle f\right\rangle_I|$ where $\left\langle f\right\rangle_I$ is the mean of $f$ over $I$. This sheds new light on the similar problem for the usual Hilbert transform that we exploit. Comment: v5: Only changes to the abstract so symbols display properly, Annales de la Facult\'e des Sciences de Toulouse. Math\'ematiques. S\'erie 6, Universit\'e Paul Sabatier \_ Cellule Mathdoc 2017 |
| Databáze: | OpenAIRE |
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