Abstract
We study big Hankel operators H_f^nu :A^p_omega rightarrow L^q_nu generated by radial Bekollé–Bonami weights nu , when 1<ple q<infty . Here the radial weight omega is assumed to satisfy a two-sided doubling condition, and A^p_omega denotes the corresponding weighted Bergman space. A characterization for simultaneous boundedness of H_f^nu and H_{{overline{f}}}^nu 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.
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