
TL;DR
This paper systematically studies operator-valued Hardy spaces within non-commutative L^p spaces linked to semifinite von Neumann algebras, motivated by matrix harmonic analysis and non-commutative martingale inequalities.
Contribution
It introduces a new framework for non-commutative Hardy spaces defined via the non-commutative Lusin integral, expanding the theoretical understanding of operator-valued harmonic analysis.
Findings
Established properties of non-commutative Hardy spaces
Connected non-commutative Hardy spaces with martingale inequalities
Provided foundational results for operator-valued harmonic analysis
Abstract
We give a systematic study on the Hardy spaces of functions with values in the non-commutative -spaces associated with a semifinite von Neumann algebra This is motivated by the works on matrix valued Harmonic Analysis (operator weighted norm inequalities, operator Hilbert transform), and on the other hand, by the recent development on the non-commutative martingale inequalities. Our non-commutative Hardy spaces are defined by the non-commutative Lusin integral function.
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Holomorphic and Operator Theory · Advanced Operator Algebra Research
