Hardy spaces of operator-valued analytic functions
Chen, Zeqian
Illinois J. Math., Tome 53 (2009) no. 1, p. 303-324 / Harvested from Project Euclid
We are concerned with Hardy and BMO spaces of operator-valued functions analytic in the unit disk of ℂ. In the case of the Hardy space, we involve the atomic decomposition since the usual argument in the scalar setting is not suitable. Several properties (the Garsia-norm equivalent theorem, Carleson measure, and so on) of BMOA spaces are extended to the operator-valued setting. Then, the operator-valued H1-BMOA duality theorem is proved. Finally, by the H1-BMOA duality we present the Lusin area integral and Littlewood–Paley g-function characterizations of the operator-valued analytic Hardy space.
Publié le : 2009-05-15
Classification:  46E40,  32A37
@article{1264170852,
     author = {Chen, Zeqian},
     title = {Hardy spaces of operator-valued analytic functions},
     journal = {Illinois J. Math.},
     volume = {53},
     number = {1},
     year = {2009},
     pages = { 303-324},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1264170852}
}
Chen, Zeqian. Hardy spaces of operator-valued analytic functions. Illinois J. Math., Tome 53 (2009) no. 1, pp.  303-324. http://gdmltest.u-ga.fr/item/1264170852/