N. Arcozzi, R. Rochberg, E. T. Sawyer, and B. D. Wick, The Dirichlet space: a survey, New York J. Math, pp.17-45, 2011.

A. Beurling, Ensembles exceptionnels, Acta Mathematica, vol.72, issue.0, pp.1-13, 1940.
DOI : 10.1007/BF02546325

T. Carroll and C. C. Cowen, Compact composition operators not in the Schatten classes, J. Operator Theory, vol.26, issue.1, pp.109-120, 1991.

J. B. Conway, Functions of One Complex Variable II, Graduate Texts in Math, 1995.

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, Exceptional sets and Hilbert???Schmidt composition operators, Journal of Functional Analysis, vol.199, issue.2, pp.287-300, 2003.
DOI : 10.1016/S0022-1236(02)00006-X

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

M. M. Jones, Compact composition operators not in the Schatten classes, Proc. Amer, pp.1947-1953, 2006.

J. P. Kahane and R. Salem, Ensembles parfaits et séries trigonométriques , nouvelle édition, 1994.

K. Kellay and P. Lefèvre, Compact composition operators on weighted Hilbert spaces of analytic functions, Journal of Mathematical Analysis and Applications, vol.386, issue.2, pp.718-727, 2012.
DOI : 10.1016/j.jmaa.2011.08.033
URL : https://hal.archives-ouvertes.fr/hal-00474028

P. Lefèvre, D. Li, H. Queffélec, and L. Rodríguez-piazza, 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> and Hardy???Orlicz spaces, Journal of Mathematical Analysis and Applications, vol.354, issue.1, pp.360-371, 2009.
DOI : 10.1016/j.jmaa.2009.01.004

P. Lefèvre, D. Li, H. Queffélec, and L. Rodríguez-piazza, Composition operators on Hardy-Orlicz spaces, Memoirs Amer, Math. Soc, vol.207, issue.974, 2010.

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, Nevanlinna counting function and Carleson function of analytic maps, Mathematische Annalen, vol.125, issue.2, pp.305-326, 2011.
DOI : 10.1007/s00208-010-0596-1

P. Lefèvre, D. Li, H. Queffélec, and L. Rodríguez-piazza, Approximation numbers of composition operators on the Dirichlet space, Arkiv f??r Matematik, vol.53, issue.1
DOI : 10.1007/s11512-013-0194-z

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, Estimates for approximation numbers of some classes of composition operators
URL : https://hal.archives-ouvertes.fr/hal-00704746

D. H. Luecking, Trace ideal criteria for Toeplitz operators, Journal of Functional Analysis, vol.73, issue.2, pp.345-368, 1987.
DOI : 10.1016/0022-1236(87)90072-3

D. H. Luecking and K. H. Zhu, Composition Operators Belonging to the Schatten Ideals, American Journal of Mathematics, vol.114, issue.5, pp.1127-1145, 1992.
DOI : 10.2307/2374892

B. Mccluer and J. Shapiro, Angular derivatives and compact composition operators on the Hardy and Bergman spaces, Canad, J. Math, vol.38, issue.4, pp.878-906, 1986.

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

W. T. Ross, The classical Dirichlet space, Contemp. Math. Amer. Math. Soc, vol.393, pp.171-197, 2006.
DOI : 10.1090/conm/393/07378

D. A. Stegenga, Multipliers on the Dirichlet space, Illinois J. Math, vol.24, issue.1, pp.113-139, 1980.

P. Wojtaszczyk, Banach spaces for analysts, Cambridge Studies in Advanced Mathematics, vol.25, 1991.
DOI : 10.1017/CBO9780511608735

X. M. Xu, Schatten-class composition operators on weighted Dirichlet spaces, Acta Anal, Funct. Appl, vol.1, issue.1, pp.86-91, 1999.

K. H. Zhu, Operator Theory in Function Spaces, Monographs and Textbooks in Pure and Applied Mathematics 139, 1990.

K. H. Zhu, Schatten class composition operators on weighted Bergman spaces of the disk, J. Operator Theory, vol.46, issue.1, pp.173-181, 2001.

N. Zorboska, Composition operators on weighted Dirichlet spaces, Proceed . Amer, Math. Soc, vol.126, issue.7, pp.2013-2023, 1998.