On Hardy kernels as reproducing kernels

Hardy kernels are a useful tool to define integral operators on Hilbertian spaces like L-2(R+) or H-2(C+). These kernels entail an algebraic L-1-structure which is used in this work to study the range spaces of those operators as reproducing kernel Hilbert spaces. We obtain their reproducing kernels, which in the L-2(R+) case turn out to be Hardy kernels as well. In the H-2(C+) scenario, the reproducing kernels are given by holomorphic extensions of Hardy kernels. Other results presented here are theorems of Paley-Wiener type, and a connection with one-sided Hilbert transforms.