A. F. Beardon and D. Minda, The hyperbolic metric and geometric function theory, Quasiconformal mappings and their applications, pp.9-56, 2007.

E. Bishop, A general Rudin-Carleson theorem, Proc. Amer, pp.140-143, 1962.
DOI : 10.1090/s0002-9939-1962-0133462-4

C. C. Cowen and B. D. Maccluer, Composition Operators on Spaces of Analytic Functions, Studies in Advanced Mathematics, 1995.

P. Duren, Theory of H p -spaces, 2000.

O. El-fallah, K. Kellay, M. Shabankhah, and H. Youssfi, Level sets and composition operators on the Dirichlet space, Journal of Functional Analysis, vol.260, issue.6, pp.1721-1733, 2011.
DOI : 10.1016/j.jfa.2010.12.023
URL : https://hal.archives-ouvertes.fr/hal-00466832

E. A. Gallardo-gutiérrez and M. J. González, Hausdorff measures, capacities and compact composition operators, Mathematische Zeitschrift, vol.253, issue.1, pp.63-74, 2006.
DOI : 10.1007/s00209-005-0878-6

J. B. Garnett, Bounded Analytic Functions, Revised first version, Graduate Texts in Math, 2007.

K. Hoffman, Banach Spaces of Analytic Functions, Prentice-Hall Series in Modern Analysis, N. J, 1962.

P. Lefèvre, D. Li, H. Queffélec, and L. Rodríguez-piazza, Some examples of compact composition operators on <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:msup><mml:mi>H</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:math>, Journal of Functional Analysis, vol.255, issue.11, pp.3098-3124, 2008.
DOI : 10.1016/j.jfa.2008.06.027

P. Lefèvre, D. Li, H. Queffélec, and L. Rodríguez-piazza, Some revisited results about composition operators on Hardy spaces, Revista Matem??tica Iberoamericana, vol.28, issue.1, pp.57-76, 2012.
DOI : 10.4171/RMI/666

P. Lefèvre, D. Li, H. Queffélec, and L. Rodríguez-piazza, Compact composition operators on Bergman-Orlicz spaces, preprint arXiv, pp.910-5368

P. Lefèvre, D. Li, H. Queffélec, and L. Rodríguez-piazza, Some new properties of composition operators associated with lens maps, Israel Journal of Mathematics, vol.121, issue.2
DOI : 10.1007/s11856-012-0164-3

D. Li, Compact composition operators on Hardy-Orlicz and Bergman-Orlicz spaces, Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas, vol.24, issue.1, pp.247-260, 2011.
DOI : 10.1007/s13398-011-0027-5
URL : https://hal.archives-ouvertes.fr/hal-00530387

D. Li, H. Queffélec, and L. Rodríguez-piazza, On approximation numbers of composition operators, Journal of Approximation Theory, vol.164, issue.4, pp.431-459, 2012.
DOI : 10.1016/j.jat.2011.12.003
URL : https://hal.archives-ouvertes.fr/hal-00588256

B. D. Maccluer, Compact composition operators on H p (B N ), Michigan Math, J, vol.32, issue.2, pp.237-248, 1985.

A. V. Megretskii, V. V. Peller, and S. R. , The inverse spectral problem for self-adjoint Hankel operators, Acta Mathematica, vol.174, issue.2, pp.241-309, 1995.
DOI : 10.1007/BF02392468

A. V. Medvedev, On a concave differentiable majorant of a modulus of continuity, Real Anal, Exchange, vol.27, issue.1, pp.123-130, 2001.

Z. Nehari, Conformal mapping, 1952.

N. K. Nikolski and . Operators, Functions and Systems: An Easy Reading, Hankel, and Toeplitz, Math. Surveys and Monographs 92, 2002.
DOI : 10.1090/surv/092

B. P. Palka, An Introduction to Complex Function Theory, Undergraduate Texts in Mathematics, 1991.
DOI : 10.1007/978-1-4612-0975-1

J. H. Shapiro, Composition Operators and Classical Function Theory, 1993.
DOI : 10.1007/978-1-4612-0887-7

D. Li, U. , L. Paul-painlevé, U. M. Cnrs, F. Villeneuve-d-'ascq-cedex et al., 2462 & Fédération CNRS Nord- Pas-de-Calais FR 2956, Faculté des Sciences Jean Perrin, Rue Jean Souvraz, S.P. 18, F-62 300 LENS, FRANCE daniel.li@euler.univ-artois.fr Hervé Queffélec Fédération CNRS Nord-Pas-de-Calais FR 2956, F-59 655, Queffelec@univ-lille1.fr Luis Rodríguez-Piazza, p.80