Bounded mean oscillation on the bidisk and the operator BMO
The authors study the BMO spaces in two variables as operator valued BMO functions in one variable and give strict inclusions in the BMO scale. In particular, it is shown that there exists a symbol \(b\) defined on the bidisk such that the little Hankel operator \(\gamma_b=P^\bot_1 P_2^\bot b P_2^\bot P_1^\bot\) is bounded on the set of all products of normalized Szegö kernels \(\{k_{z_1}\otimes{k_{z_2}}: z_1, z_2 \in D\}\) but does not extend to a bounded linear operator on \(H^2 (T^2)\).
scientific article; zbMATH DE number 1797577