Abstract
Bounded Bergman projections $$P_\omega:L_\omega^p(v)\rightarrow{L_\omega^p(v)}$$ , induced by reproducing kernels admitting the representation $$\frac{1}{(1-\overline{z}\zeta)^\gamma}\int_{0}^{1} \frac{dv(r)}{1-r\overline{z}\zeta},\;\;0\leq{r}<1,$$ and the corresponding (1,1)-inequality are characterized in terms of Bekolle-Bonami-type conditions. The two-weight inequality for the maximal Bergman projection $$P_\omega^+:L_\omega^p(u)\rightarrow{L_\omega^p(v)}$$ in terms of Sawyer-testing conditions is also discussed.
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