El Teorema de Brown-Shields-Zeller

Abstract

[en] In this memoir we will prove the extension of the Brown-Shields-Zeller Theorem to $H^p$, which states that a sequence in the unit disk $\mathbb{D}$ is sampling for the Hardy space $H^p$ if and only if almost every point of the unit circle is a non-tangential limit point of the sequence. To prove this result we will base our study in the Harmonic analysis, in particular the study of harmonic functions and Poisson kernels and integrals, which will play an important role in the work. Finally, we will finish with a factorization on the Hardy spaces to give way to the proof of Brown-Shields-Zeller.