$L^p$ Regularity of Some Weighted Bergman Projections on the Unit Disc

We show that weighted Bergman projections, corresponding to weights of the form $M(z)(1-\mathrm{\mid }z{\mathrm{\mid }}^2{)}^{\alpha }$ where $\alpha >-1$ and $M(z)$ is a radially symmetric, strictly positive and at least $C^2$ function on the unit disc, are $L^p$ regular.