Hankel operators induced by radial Bekollé–Bonami weights on Bergman spaces

We study big Hankel operators $$H_f^\nu :A^p_\omega \rightarrow L^q_\nu $$ H f ν : A ω p → L ν q generated by radial Bekollé–Bonami weights $$\nu $$ ν , when $$1<p\le q<\infty $$ 1 < p ≤ q < ∞ . Here the radial weight $$\omega $$ ω is assumed to satisfy a two-sided doubling condition, and $$A^p_\omega $$ A ω p denotes the corresponding weighted Bergman space. A characterization for simultaneous boundedness of $$H_f^\nu $$ H f ν and $$H_{{\overline{f}}}^\nu $$ H f ¯ ν 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 $$\omega $$ ω and $$\nu $$ ν 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.