Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2602.24186 |
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Inhaltsangabe:
- We prove an $\LlogL $-type distributional inequality for the commutator of the Bergman projection with a conjugate Bloch symbol function on the unit ball. Such an inequality can be seen as a Bergman version of a result due to C. Pérez for real-variable Calderón-Zygmund operators and BMO functions. We also prove that this inequality characterizes membership of analytic functions in the Bloch space and is further equivalent to a kind of modified restricted weak-type estimate, where one only tests over characteristic functions of sets comparable to Bergman balls. We also show our estimate is sharp in the sense that there exists a Bloch function $b$ so that the commutator $[\bar{b},P]$ is not weak-type $(1,1)$, and prove $[\bar{b},P]$ with $b$ analytic is weak-type $(1,1)$ if and only if $b \in H^\infty$.