Exponentially weighted LpLp-estimates for ∂¯ on the unit disc

We prove the LpLp-estimates for the ∂¯-equation in the exponentially weighted LpLp-spaces on the unit disc. These estimates are extensions of the classical Hörmander weighted L2L2-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.