English

Embedding $H^\infty(\D)$ into $L^\infty(\T)$: a proof without non-tangential limits

Functional Analysis 2025-11-21 v1

Abstract

The purpose of this note is to show in an accessible and self-contained way the existence of an isometric algebra embedding from H(\D)H^\infty(\D) into L(\T)L^\infty(\T), without appealing to Fatou's classical theorem on non-tangential limits of analytic functions, and relying only on results from complex and functional analysis that are typically covered in a standard undergraduate course.

Keywords

Cite

@article{arxiv.2511.16489,
  title  = {Embedding $H^\infty(\D)$ into $L^\infty(\T)$: a proof without non-tangential limits},
  author = {Mario P. Maletzki},
  journal= {arXiv preprint arXiv:2511.16489},
  year   = {2025}
}
R2 v1 2026-07-01T07:47:31.132Z