Riemann-Stieltjes operators between different weighted Bergman spaces

Abstract

Let $g:B\to \mathbb C^1$ be a holomorphic map of the unit ball $B$. We give a complete picture regarding the boundedness and compactness of the following two integral operators $$ T_gf(z)=\int_0^1f(tz)\Re g(tz)\frac{dt}{t}\text{ and } L_gf(z)= \int_0^1 \Re f(tz) g(tz)\frac{dt}{t},\quad z\in B, $$ between different weighted Bergman spaces.