For 00 such that ᵣ¹ω (s) ds C ₁+ₑ₂¹ω (s) \, ds \, \, for every\, \, 0 r <1. We describe the dual space of A^p, q_ω for every 0<p, q< and ωD. Later on, we apply the obtained description of the dual space of A^p, q_ω to prove that the Bergman projection induced by ω, P_ω, is bounded on L^p, q_ω for 1<p, q< and ω D. Besides, we also prove that P_ω and the corresponding maximal Bergman projection P_ω^+ are not simultaneously bounded on L^p, q_ω for 1<p, q< and ω D.
Moreno et al. (Tue,) studied this question.