Resumen de Hankel operators in several complex variables and product "BMO"

Michael T. Lacey, Erin Terwilleger

• We consider the Hilbertian Hardy space on the product of tori, and the "little" Hankel operator which maps these spaces into themselves. These operators are indexed by their symbol b, a function that can be taken to be jointly analytic in all the variables present. We show that these operators are bounded iff the symbol b is in Chang-Fefferman BMO, genearlizing the classical result of Nehari, and a recent result of S. Ferguson and one of the authors on the bi-disk. This result is proved by an argument which inducts on the number of complex variables present. This is is carried out with a particular form of a Journe Lemma, which occurs implicitly in the work of Pipher.