Reverse Carleson measures in Hardy spaces

Andreas Hartmann; Xavier Massaneda; Artur Nicolau; Joaquim Ortega-Cerdà

doi:https://doi.org/10.1007/s13348-014-0105-z

Reverse Carleson measures in Hardy spaces

Andreas Hartmann, Xavier Massaneda, Artur Nicolau, Joaquim Ortega-Cerdà

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

4 Citations (Scopus)

Abstract

We give a necessary and sufficient condition for a measure μ in the closed unit disk to be a reverse Carleson measure for Hardy spaces. This extends a previous result of Lefèvre, Li, Queffélec and Rodríguez-Piazza Lefèvre et al. (Rev Mat Iberoam 28(1):57-76, 2012). We also provide a simple example showing that the analogue for the Paley-Wiener space does not hold. As it turns out the analogue never holds in any model space. © 2014 Universitat de Barcelona.

Original language	English
Pages (from-to)	357-365
Journal	Collectanea Mathematica
Volume	65
DOIs	https://doi.org/10.1007/s13348-014-0105-z
Publication status	Published - 1 Jan 2014

Keywords

Carleson measure
Hardy space
Model space
Reproducing kernel
Reproducing kernel thesis
Reverse Carleson measure

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title = "Reverse Carleson measures in Hardy spaces",

abstract = "We give a necessary and sufficient condition for a measure μ in the closed unit disk to be a reverse Carleson measure for Hardy spaces. This extends a previous result of Lef{\`e}vre, Li, Queff{\'e}lec and Rodr{\'i}guez-Piazza Lef{\`e}vre et al. (Rev Mat Iberoam 28(1):57-76, 2012). We also provide a simple example showing that the analogue for the Paley-Wiener space does not hold. As it turns out the analogue never holds in any model space. {\textcopyright} 2014 Universitat de Barcelona.",

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AU - Hartmann, Andreas

AU - Massaneda, Xavier

AU - Nicolau, Artur

AU - Ortega-Cerdà, Joaquim

PY - 2014/1/1

Y1 - 2014/1/1

N2 - We give a necessary and sufficient condition for a measure μ in the closed unit disk to be a reverse Carleson measure for Hardy spaces. This extends a previous result of Lefèvre, Li, Queffélec and Rodríguez-Piazza Lefèvre et al. (Rev Mat Iberoam 28(1):57-76, 2012). We also provide a simple example showing that the analogue for the Paley-Wiener space does not hold. As it turns out the analogue never holds in any model space. © 2014 Universitat de Barcelona.

AB - We give a necessary and sufficient condition for a measure μ in the closed unit disk to be a reverse Carleson measure for Hardy spaces. This extends a previous result of Lefèvre, Li, Queffélec and Rodríguez-Piazza Lefèvre et al. (Rev Mat Iberoam 28(1):57-76, 2012). We also provide a simple example showing that the analogue for the Paley-Wiener space does not hold. As it turns out the analogue never holds in any model space. © 2014 Universitat de Barcelona.

KW - Carleson measure

KW - Hardy space

KW - Model space

KW - Reproducing kernel

KW - Reproducing kernel thesis

KW - Reverse Carleson measure

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DO - https://doi.org/10.1007/s13348-014-0105-z

M3 - Article

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SP - 357

EP - 365

ER -