Hankel operators induced by radial Bekolle-Bonami weights on Bergman spaces

Journal article, 2020

We study big Hankel operators H-f(nu) : A(omega)(p) -> L-nu(q) generated by radial Bekolle-Bonami weights nu, when 1 < p <= q < infinity. Here the radial weight omega is assumed to satisfy a two-sided doubling condition, and A(omega)(p) denotes the corresponding weighted Bergman space. A characterization for simultaneous boundedness of H-f(nu) and H nu/f is provided in terms of a general weighted mean oscillation. Compared to the case of standard weights that was recently obtained by Pau et al. (Indiana Univ Math J 65(5):1639-1673, 2016), the respective spaces depend on the weights omega and nu in an essentially stronger sense. This makes our analysis deviate from the blueprint of this more classical setting. As a consequence of our main result, we also study the case of anti-analytic symbols.