On planar Beurling and Fourier transforms

Abstract

We study the Beurling and Fourier transforms on subspaces of $L^2(\mathbb{C})$ defined by an invariance property with respect to the root-of-unity group. This leads to generalizations of these transformations acting unitarily on weighted $L^2$-spaces over $\mathbb{C}$.

10 pages

References in corpus (1)

• Boundary properties of Green functions in the plane