Reverse Carleson measures in Hardy spaces

Andreas Hartmann (1) , Xavier Massaneda (2) , Artur Nicolau (3) , Joaquim Ortega-Cerdà (4)

1 IMB - Institut de Mathématiques de Bordeaux
2 Departament de Matemàtica Aplicada i Anàlisi
3 UAB - Departament de Matemàtiques [Barcelona]
4 Departament de Matemàtica Aplicada i Anàlisi [Barcelona]

We give a necessary and sufficient condition for a measure $\mu$ in the closed unit disk to be a reverse Carleson measure for Hardy spaces. This extends a previous result of Lefévre, Li, Queffélec and Rodr\'{\i}guez-Piazza \cite{LLQR}. We also provide a simple example showing that the analogue for the Paley-Wiener space does not hold. This example can be generalised to model spaces associated to one-component inner functions.

Mots clés: Hardy space; Carleson measure; reverse Carleson measure; reproducing kernel; reproducing kernel thesis; model space

Domaines: Variables complexes [math.CV]

Andreas Hartmann, Xavier Massaneda, Artur Nicolau, Joaquim Ortega-Cerdà. Reverse Carleson measures in Hardy spaces. Collectanea Mathematica, 2014, 65 (3), pp.357-365. ⟨hal-00808063⟩