Small Hankel operator induced by measurable symbol acting on weighted Bergman spaces

The boundedness of the small Hankel operator h^ωf(g)=P_ω̄(fg) induced by a measurable symbol f and the Bergman projection P_ω associated to a radial weight ω acting from the weighted Bergman space Aᵖ_ω to its conjugate analytic counterpart Aᵖ_ω̄ is characterized on the range 1<p<∞ when ω belongs to the class D of radial weights admitting certain two-sided doubling conditions. On the way to the proof a sharp integral estimate for certain modified Bergman kernels is obtained.