[Absolutely summing Carleson embedding]
We study the Carleson embeddings on the Hardy spaces with . We characterize their membership in the class of r-summing operators for any . This generalizes in a strong way former results and solves a problem open since the 1970s. This characterization is different in nature according to the value of the couple . As particular cases, this settles the case of composition and weighted composition operators.
Nous étudions les plongements de Carleson sur les espaces de Hardy où . Nous caractérisons leur appartenance à la classe des opérateurs r-sommants quelle que soit la valeur de . Ceci généralise complètement des résultats antérieurs et résout un problème ouvert depuis les années 1970. Cette caractérisation est de nature différente suivant la valeur du couple . Ces résultats englobent le cas des opérateurs de composition, et des opérateurs de composition à poids.
Accepted:
Published online:
Pascal Lefèvre 1; Luis Rodríguez-Piazza 2
@article{CRMATH_2016__354_12_1209_0, author = {Pascal Lef\`evre and Luis Rodr{\'\i}guez-Piazza}, title = {Plongements de {Carleson} absolument sommants}, journal = {Comptes Rendus. Math\'ematique}, pages = {1209--1213}, publisher = {Elsevier}, volume = {354}, number = {12}, year = {2016}, doi = {10.1016/j.crma.2016.10.010}, language = {fr}, }
Pascal Lefèvre; Luis Rodríguez-Piazza. Plongements de Carleson absolument sommants. Comptes Rendus. Mathématique, Volume 354 (2016) no. 12, pp. 1209-1213. doi : 10.1016/j.crma.2016.10.010. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.10.010/
[1] Composition Operators on Spaces of Analytic Functions, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, États-Unis, 1995
[2] Absolutely Summing Operators, Cambridge University Press, Cambridge, Royaume-Uni, 1995
[3] Composition operators belonging to operator ideals, J. Math. Anal. Appl., Volume 237 (1999) no. 1, pp. 327-349
[4] Absolutely summing Carleson embeddings, 2016 | arXiv
[5] Composition Operators and Classical Function Theory, Universitext: Tracts in Mathematics, Springer-Verlag, New York, 1993
[6] Compact, nuclear, and Hilbert–Schmidt composition operators on , Indiana Univ. Math. J., Volume 23 (1973) no. 6, pp. 471-496
Cited by Sources:
Comments - Policy