A Weighted L2-Estimate for the Green-Faddeev Function for the Laplace Operator in R2

This paper studies the behavior of the Green-Faddeev function gz(x) in R2 With z ∈ C2/R2 and z • z ≥ 0. It is shown that the convolution operator Dαgz ∗ (|α| ≤ 2) acting on suitable weighted L2-spaces has a norm dominated by O(|z||α|−1A (|Re z|/|Im z|)) with a positive function A (r)(r ≥ 0) if |z| → ∞ and z • z ≥ 0.