On operator valued Hardy spaces

Denis Potapov

On operator valued Hardy spaces

Functional Analysis 2010-12-09 v2

Authors: Denis Potapov

Abstract

The note shows that the operator-valued Hardy space $\sH^1$ introduced via Littlewood-Paley $g$ -function coincides with the space of $H^1_R(\T, \sL^1)$ of all Bochner integrable operator-valued functions with integrable analytic part. The proof is based on the noncommutative maximal inequality for Poisson group.

Keywords

hardy spaces operator theory

Cite

@article{arxiv.1011.6209,
  title  = {On operator valued Hardy spaces},
  author = {Denis Potapov},
  journal= {arXiv preprint arXiv:1011.6209},
  year   = {2010}
}

Comments

This paper has been withdrawn by the author. The current argument has an error. The current result implies that every Calderon-Zygmund operator is bounded on H^1(T, S^1) which is, in fact, not the case

On operator valued Hardy spaces

Abstract

Keywords

Cite

Comments

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