Exponentially weighted -estimates for on the unit disc

We prove the L p -estimates for the ∂ ¯ -equation in the exponentially weighted L p -spaces on the unit disc. These estimates are extensions of the classical Hörmander weighted L 2 -estimates. We use only a family of holomorphic peak functions with precise growth conditions, which is technically simpler than using multipliers as was done by others in obtaining earlier results.