Let be a bounded, circular and strictly convex domain with the boundary of class . Denote by the space of all holomorphic functions in Ω. Given and a holomorphic mapping , put for . We characterize those g and φ for which is a bounded or compact operator from the growth space or , , to the weighted Bergman space , , . Also, given and , we describe those positive measures μ on Ω for which and those μ for which .
Soit Ω un domaine circulaire, strictement convexe et borné dans dont le bord est de classe . Nous désignons par l'espace des fonctions holomorphes dans Ω. Soient et une transformation holomorphe. Posons pour . Nous caractérisons les fonctions g et φ pour lesquelles est un opérateur borné ou compact de l'espace à croissance ou de , , dans l'espace de Bergman à poids , , . Nous caractérisons aussi les mesures positives μ sur Ω telles que et les mesures positives μ telles que pour et .
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@article{CRMATH_2009__347_11-12_609_0, author = {Doubtsov, Evgueni}, title = {Growth spaces on circular domains: composition operators and {Carleson} measures}, journal = {Comptes Rendus. Math\'ematique}, pages = {609--612}, publisher = {Elsevier}, volume = {347}, number = {11-12}, year = {2009}, doi = {10.1016/j.crma.2009.04.003}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.crma.2009.04.003/} }
TY - JOUR AU - Doubtsov, Evgueni TI - Growth spaces on circular domains: composition operators and Carleson measures JO - Comptes Rendus. Mathématique PY - 2009 SP - 609 EP - 612 VL - 347 IS - 11-12 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2009.04.003/ DO - 10.1016/j.crma.2009.04.003 LA - en ID - CRMATH_2009__347_11-12_609_0 ER -
%0 Journal Article %A Doubtsov, Evgueni %T Growth spaces on circular domains: composition operators and Carleson measures %J Comptes Rendus. Mathématique %D 2009 %P 609-612 %V 347 %N 11-12 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2009.04.003/ %R 10.1016/j.crma.2009.04.003 %G en %F CRMATH_2009__347_11-12_609_0
Doubtsov, Evgueni. Growth spaces on circular domains: composition operators and Carleson measures. Comptes Rendus. Mathématique, Volume 347 (2009) no. 11-12, pp. 609-612. doi : 10.1016/j.crma.2009.04.003. http://www.numdam.org/articles/10.1016/j.crma.2009.04.003/
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