Extension domains for Hardy spaces
Shahaboddin Shaabani

TL;DR
This paper characterizes when open subsets of Euclidean space are extension domains for Hardy spaces $H^p$, linking geometric conditions to the existence of linear extension operators, and explores implications for subspaces of BMO.
Contribution
It provides a complete geometric characterization of extension domains for $H^p$ spaces and establishes the existence of linear extension operators under these conditions.
Findings
Proper open subsets are extension domains iff they satisfy a specific geometric condition.
When $n(1/p - 1)$ is an integer, the condition aligns with the global Markov condition.
For certain $p$, all proper open subsets are extension domains.
Abstract
We show that a proper open subset is an extension domain for (), if and only if it satisfies a certain geometric condition. When this condition is equivalent to the global Markov condition for , for it is stronger, and when every proper open subset is an extension domain for . It is shown that in each case a linear extension operator exists. We apply our results to study some complemented subspaces of .
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsHolomorphic and Operator Theory · Advanced Harmonic Analysis Research · Advanced Banach Space Theory
