Linear Poisson Equations with Potential on Riemann Surfaces

We study interior estimates for solutions of the linear Poisson equation: $$\mathrm{△}u=gu+f$$ where $g$ and $f$ belong to the Zygmund space $L\ln L$ on a Riemann surface $M$ satisfying the isoperimetric inequality. As applications, we derive corresponding interior estimates, Harnack inequalities, and a global estimate.