Calderón-Zygmund theory with noncommuting kernels via \(\text{H}_1^c\). (English) Zbl 07927016
Summary: We study an alternative definition of the \(\text{H}_1\)-space associated to a semicommutative von Neumann algebra \(L_\infty (\mathbb{R}) \overline{\otimes} \mathcal{M}\), first studied by T. Mei [Operator valued Hardy spaces. Providence, RI: American Mathematical Society (AMS) (2007; Zbl 1138.46038)]. We identify a “new” description for atoms in \(\text{H}_1\). We then explain how they can be used to study \(\text{H}_1^c - L_1\) endpoint estimates for Calderón-Zygmund operators with noncommuting kernels.
MSC:
| 42B20 | Singular and oscillatory integrals (Calderón-Zygmund, etc.) |
| 42B35 | Function spaces arising in harmonic analysis |
| 46L51 | Noncommutative measure and integration |
| 46L52 | Noncommutative function spaces |
Keywords:
Hardy space; BMO space; von Neumann algebra; non-commutative \(L_p\) space; Calderón-Zygmund theory; atomsCitations:
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| [28] | Antonio Ismael Cano-Mármol Department of Mathematics Baylor University Waco, TX 76798, USA E-mail: AntonioIsmael_CanoMa@baylor.edu Éric Ricard Laboratoire de Mathématiques Nicolas Oresme UNICAEN, CRNS 1400 Caen, France E-mail: eric.ricard@unicaen.fr |
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