naa a22 4500 510810489 CHVBK 20180411083440.0 cr unu---uuuuu 180411e20130101xx s 000 0 eng 10.1007/s12220-011-9241-9 doi (NATIONALLICENCE)springer-10.1007/s12220-011-9241-9 Hankel Operators on Fock Spaces and Related Bergman Kernel Estimates [Elektronische Daten] [Kristian Seip, El Youssfi] Hankel operators with anti-holomorphic symbols are studied for a large class of weighted Fock spaces on ℂ n . The weights defining these Hilbert spaces are radial and subject to a mild smoothness condition. In addition, it is assumed that the weights decay at least as fast as the classical Gaussian weight. The main result of the paper says that a Hankel operator on such a Fock space is bounded if and only if the symbol belongs to a certain BMOA space, defined via the Berezin transform. The latter space coincides with a corresponding Bloch space which is defined by means of the Bergman metric. This characterization of boundedness relies on certain precise estimates for the Bergman kernel and the Bergman metric. Characterizations of compact Hankel operators and Schatten class Hankel operators are also given. In the latter case, results on Carleson measures and Toeplitz operators along with Hörmander's L 2 estimates for the $\bar{\partial}$ operator are key ingredients in the proof. Mathematica Josephina, Inc., 2011 Bergman kernel nationallicence Hankel operator nationallicence Fock space nationallicence Seip Kristian Department of Mathematical Sciences, Norwegian University of Science and Technology (NTNU), 7491, Trondheim, Norway aut Youssfi El LATP, U.M.R. C.N.R.S. 6632, CMI, Université de Provence, 39 Rue F-Joliot-Curie, 13453, Marseille Cedex 13, France aut Journal of Geometric Analysis Springer-Verlag 23/1(2013-01-01), 170-201 1050-6926 23:1<170 2013 23 12220 https://doi.org/10.1007/s12220-011-9241-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s12220-011-9241-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Seip Kristian Department of Mathematical Sciences, Norwegian University of Science and Technology (NTNU), 7491, Trondheim, Norway aut NATIONALLICENCE 700 1- Youssfi El LATP, U.M.R. C.N.R.S. 6632, CMI, Université de Provence, 39 Rue F-Joliot-Curie, 13453, Marseille Cedex 13, France aut NATIONALLICENCE 773 0- Journal of Geometric Analysis Springer-Verlag 23/1(2013-01-01), 170-201 1050-6926 23:1<170 2013 23 12220 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer