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We study big Hankel operators $H_f^\nu:A^p_\omega \to L^q_\nu$ generated byradial Bekoll\'e-Bonami weights $\nu$, when $1<p\leq q<\infty$. Here the radialweight $\omega$ is assumed to satisfy a two-sided doubling condition, and$A^p_\omega$ denotes the corresponding weighted Bergman space. Acharacterization for simultaneous boundedness of $H_f^\nu$ and$H_{\overline{f}}^\nu$ is provided in terms of a general weighted meanoscillation. Compared to the case of standard weights that was recentlyobtained by Pau, Zhao and Zhu (Indiana Univ. Math. J. 2016), the respectivespaces depend on the weights $\omega$ and $\nu$ in an essentially strongersense. This makes our analysis deviate from the blueprint of this moreclassical setting. As a consequence of our main result, we also study the caseof anti-analytic symbols.

Hankel operators induced by radial Bekoll\'e-Bonami weights on Bergman spaces